TW201732452A - Optical system and method - Google Patents

Abstract

An optical system comprising: an illumination system configured, to form a periodic illumination mode comprising radiation in a pupil plane of the optical system having a spatial intensity profile which is periodic in at least one direction, a measurement system configured to measure a dose of radiation which is received in an field plane of the optical system as a function of position in the field plane, and a controller configured to: select one or more spatial frequencies in the field plane at which variation in the received dose of radiation as a function of position is caused by speckle, and determine a measure of the variation of the received dose of radiation as a function of position at the selected one or more spatial frequencies, the measure of the variation in the received dose being indicative of speckle in the field plane.

Description

Optical system and method

The present invention relates to an optical system and a method of performing the measurement. The optical system can form part of the lithography apparatus particularly, but not exclusively.

The lithography apparatus is a machine that applies a desired pattern to a target portion of a substrate. The lithography apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that case, a patterned device (which is alternatively referred to as a reticle or pleated reticle) can be used to create a circuit pattern corresponding to individual layers of the IC, and can be imaged to have a radiation-sensitive material (resist A target portion (for example, a portion including a crystal grain, a crystal grain or a plurality of crystal grains) on a substrate (for example, a germanium wafer) of a layer. In general, a single substrate will contain a network of adjacent target portions that are sequentially exposed. Known lithography apparatus includes a so-called stepper in which each target portion is irradiated by exposing the entire pattern to a target portion at a time; and a so-called scanner in which a given direction ("scanning" Each of the target portions is irradiated by scanning the pattern via the light beam while scanning the pattern in parallel or anti-parallel in this direction while scanning the substrate in synchronization. One or more properties of the radiation propagating through the lithography device may need to be measured. There is a need to provide apparatus and methods for preventing or mitigating one or more of the prior art problems identified herein or elsewhere.

In accordance with a first aspect of the present invention, an optical system is provided, comprising: an illumination system configured to form a periodic illumination mode comprising one of the optical systems in a pupil plane Radiation having a spatial intensity profile that is periodic in at least one direction; a metrology system configured to measure a position received in a field plane of the optical system in the field plane a varying radiation dose; and a controller configured to: select a change in the received radiation dose that varies depending on the position in the field plane by one or more spatial frequencies at which the spot is located; A measure of the change in the received radiation dose as a function of position is determined at the selected one or more spatial frequencies, the measure of the change in the received dose indicating a spot in the field plane. The periodic illumination pattern formed by the illumination system is used to limit the effect of the spot to a limited number of spatial frequencies in the field plane of the optical system. The change in the received radiation dose that can vary in position in the field plane is a change in one of the radiation doses received in the field plane at one or more spatial frequencies at which the spot is caused. This change in radiation dose can, for example, correspond to a local maximum value that corresponds to one of the autocorrelation functions in which the spot is located. Advantageously, limiting the effect of the spot to a limited spatial frequency will allow the contribution of the spot to one of the dose variations in the field plane to be separated from the contribution of other effects. A plane can be an image plane or an object plane of the optical system. A pupil plane of an optical system is a plane having a Fourier relationship with a field plane. That is, each spatial point in a pupil plane corresponds to an angle in a corresponding field plane, and vice versa. The illumination system can be configured to illuminate a patterned device using a radiation beam, the patterned device configured to impart a pattern to the radiation beam in a cross-section of the radiation beam to form a patterned radiation beam. The optical system can further include a projection system configured to project a beam of radiation onto a field plane. The radiation beam projected onto the field plane can, for example, be patterned by the patterned device to pattern one of the radiation beams. The controller can be further configured to determine a contribution of the spot to the change in the received dose, the contribution of the spot being the measure of the change in the received dose at the selected one or more spatial frequencies Determined. The determined contribution of the spot to the change in the received dose may comprise a variance of the dose caused by the spot. The controller can be configured to determine one of the independent spot patterns received in the field plane for a given period of time from the measure of the change in the received dose at the selected one or more spatial frequencies number. The metrology system can include: a substrate stage configured to hold a substrate substantially in the field plane to expose the substrate to the patterned radiation beam; and a sensor configured Detecting a dimension of one of the features patterned into the substrate at different locations on the substrate, the size of the feature patterned into the substrate as a function of position on the substrate is provided The received in the field plane is measured as one of the radiation doses that vary according to the position in the field plane. The sensor can include: a scanning electron microscope configured to acquire an image of the feature patterned onto the substrate; and a controller configured to detect the image from the image One of the features at different locations. The metrology system can further include a coating development system configured to apply a resist to a substrate and develop the resist after exposure to a patterned radiation beam to The pattern is transferred to the substrate. The controller can be configured to determine an autocorrelation function of a first series and a second series, wherein the first series includes the measured location in the field plane at different locations in the field plane A radiation dose is received, and the second series is identical to the first series and offset from the first series by a position offset. The controller can be configured to evaluate the autocorrelation function at a position offset for one of the inverse of the one or more selected spatial frequencies. The position offset for the reciprocal of the one or more selected spatial frequencies may indicate that the autocorrelation function is substantially at a position offset of one local maximum. The autocorrelation function evaluated at a positional offset for the reciprocal of the one or more selected spatial frequencies may provide a change in one of the received radiation doses depending on the position in the field plane. A measure of this contribution. The controller is further configurable to scale the autocorrelation function evaluated at a position offset for the inverse of the one or more selected spatial frequencies and to determine the spot caused by the spot in the field plane The total variance of the received radiation dose. The controller can be further configured to: determine a ratio of a local maximum to a global maximum corresponding to a change in one of the doses in the field plane caused by the spot; and The autocorrelation function evaluated at a position offset for the reciprocal of the one or more selected spatial frequencies is scaled according to the determined ratio. The optical system can further include a sensor device configured to measure the spatial intensity profile of the periodic illumination pattern in the pupil plane of the optical system, wherein the controller is grouped The state determines a ratio of a local maximum value to a global maximum value in a spot autocorrelation function from the measured spatial intensity profile of the periodic illumination mode, wherein the spot autocorrelation function corresponds to the field plane It is only a change in the dose caused by the spot. The controller can be configured to perform a simulation of one of the radiation propagating through the optical system, and from the simulation determine one of the spot autocorrelation functions corresponding to one of the doses caused by only the spot in the field plane The ratio of the local maximum to a global maximum. The optical system can further include a radiation source configured to provide a radiation beam to the illumination system, wherein the radiation source is operative to adjust an attribute of the radiation beam to change the field plane per unit time The number of independent spot patterns received in . The radiation source can be configured to provide a pulsed radiation beam to the illumination system, and wherein the radiation source is operative to adjust a duration of a pulse of radiation emitted from the radiation source, thereby changing the per unit time The number of independent spot patterns received in the field plane. For each configuration of the adjustable property of the radiation source, the controller is configured to: select a change in the received radiation dose that varies according to location in the field plane by one of the spots or a plurality of spatial frequencies; and a measure of the change in the received radiation dose as a function of position at the selected one or more spatial frequencies, the measure of the change in the received dose indicating the field plane Light spot. The controller is further configurable to evaluate the measure of the change in the received dose under a plurality of configurations of the adjustable property of the radiation source, and the spot pair is determined from the evaluation in each configuration This contribution of the change in the dose received by the site. The controller can be configured to use the number of periods of the spatial intensity distribution in the pupil plane of the optical system to select the change in the measured dimension in the field plane that is caused by the spot Or multiple spatial frequencies. The controller may be configured to calculate a spatial period by P _s is selected according to the following equation by measuring the coefficient of variation of the size of the field plane of causing the one or more spatial frequencies of the light spot in which: Where K is the number of periods of the spatial intensity distribution in the pupil plane of the optical system, λ is the wavelength of the radiation beam and NA is the numerical aperture of the optical system, wherein the measurement is in the field plane Alteration of the size of the light spot caused by the one or more spatial frequencies for which the reciprocal of the spatial period P _s. The illumination system can include a mirror array that is adjustable to adjust the spatial intensity profile in the pupil plane of the optical system. The illumination system can be configured to form a periodic illumination pattern comprising radiation in a pupil plane of the optical system, the radiation having a periodic spatial intensity profile in a first direction, Wherein the periodic spatial intensity profile comprises K cycles. The illumination system can be configured such that the spatial intensity profile substantially follows a Gaussian distribution in a second direction, wherein the second direction is substantially perpendicular to the first direction. K can be an integer. K can be an odd number. K can be 5 or more. K can be 17 or less. The lighting system can be configured to form a dipole illumination mode. The optical system can include a lithography device. The patterned device can be an attenuated phase shift mask. According to a second aspect of the present invention, there is provided a method of measuring a spot in an optical system, the optical system comprising an illumination system configured to adjust a radiation beam, the method comprising: configuring the illumination system to Forming a periodic illumination mode comprising radiation in a pupil plane of the optical system, the radiation having a spatial intensity profile that is periodic in at least one direction; measuring in a field of the optical system a radiation dose received in the plane that varies according to the position in the field plane; the change in the received radiation dose that varies depending on the position in the field plane is selected by the spot to cause one or more spatial frequencies And determining, at the selected one or more spatial frequencies, a measure of the change in the received radiation dose as a function of position, the measure of the change in the size indicating the spot in the field plane. According to a third aspect of the present invention, there is provided a method of measuring a spot in a lithography apparatus, the method comprising: forming a periodic illumination mode of radiation; patterning the radiation using a pattern comprising a grating; Projecting the patterned radiation onto a substrate to form an image of the grating; measuring a line width variation of the line of the imaged grating; and performing such correlation with the line and its associated line with the other lines of the image One of the line widths is two-dimensionally related. The method can further include determining a ratio of one of a local maximum to one of a center maximum for one or more lines associated with the other line of the image; and using the ratio to include a local area for the line associated with itself The maximum value is used to determine a central maximum caused by the spot for the lines associated with itself. The method can further include using a previously performed calibration to convert the magnitude of the center maximum to one of the dose changes caused by the spot. Advantageously, the method of the third aspect of the invention does not require one of the effects of the spot to simulate, or one of the intensity distributions of the illumination mode in a pupil plane. According to a fourth aspect of the present invention, there is provided a method of measuring a spot in a lithography apparatus, the method comprising: forming a periodic illumination mode of radiation; patterning the radiation using a pattern comprising a grating; Projecting the patterned radiation onto a substrate to form an image of the grating; measuring a change in position of the line of the imaged grating; and performing the positional change associated with the line and associated with other lines of the image One of the two-dimensional correlations. According to a fifth aspect of the present invention, there is provided a method of measuring a spot in a lithography apparatus, the method comprising: forming a quadrupole illumination mode of radiation; patterning using a pattern comprising one of a two-dimensional array of features Generating the radiation; projecting the patterned radiation onto a substrate to form an image; performing a two-dimensional correlation of one of the critical dimensions of the imaged pattern features according to the pattern feature; determining that the center is far from the center of the correlation function The size of one of the correlation functions of the value; and the use of this size for the same previously obtained ratio to determine the magnitude of the central maximum of one of the correlation functions caused by the spot. Advantageously, the method of the fifth aspect of the invention does not require one of the effects of the spot to simulate, or one of the intensity distributions of the illumination mode in a pupil plane. According to a sixth aspect of the present invention, there is provided a method of measuring a spot in a lithography apparatus, the method comprising: forming a quadrupole illumination mode of radiation; patterning using a pattern comprising one of a two-dimensional array of features Generating the radiation; projecting the patterned radiation onto a substrate to form an image; performing a two-dimensional correlation of one of the positions of the imaged pattern features according to the pattern feature; determining a center maximum away from the correlation function One of the correlation functions is sized; and the same previously obtained ratio is used to determine the magnitude of the center maximum of one of the correlation functions caused by the spot. Advantageously, the method of the sixth aspect of the invention does not require one of the effects to be simulated, or one of the intensity distributions of the illumination modes in a pupil plane. The fifth aspect or the sixth aspect of the method can further include using a previously performed calibration to convert the magnitude of the center maximum to one of the dose changes caused by the spot. One or more aspects of the invention may include one or more of any of the other aspects of the invention.

Although reference may be made specifically to the use of lithography devices in IC fabrication herein, it should be understood that the lithographic devices described herein may have other applications, such as fabricating integrated optical systems for magnetic domain memory. Guide and detect patterns, liquid crystal displays (LCDs), thin film heads, and more. Those skilled in the art should understand that in the context of the content of such alternative applications, any use of the terms "wafer" or "die" herein may be considered as the more general term "substrate" or "target portion". Synonymous. The substrate referred to herein may be treated prior to or after exposure, for example, in a coating development system (a tool that typically applies a resist layer to a substrate and develops a exposed resist) or a metrology tool or inspection tool. . Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Additionally, the substrate can be processed more than once, for example, to create a multi-layer IC, such that the term substrate as used herein may also refer to a substrate that already contains multiple processed layers. The substrate can be held by the substrate stage. The terms "radiation" and "beam" as used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (for example, having 365 nm, 248 nm, 193 nm, 157 nm or 126 nm). The wavelength) and extreme ultraviolet (EUV) radiation (for example, having a wavelength in the range of 4 nm to 20 nm); and a particle beam (such as an ion beam or an electron beam). The term "patterned device" as used herein shall be interpreted broadly to mean a device that can be used to impart a pattern to a radiation beam in a cross-section of a radiation beam to produce a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate. Typically, the pattern imparted to the radiation beam will correspond to a particular functional layer in the device (such as an integrated circuit) produced in the target portion. The patterned device can be transmissive or reflective. Examples of patterned devices include photomasks, programmable mirror arrays, and programmable LCD panels. Photomasks are well known in lithography and include reticle types such as binary, alternating phase shift and attenuated phase shift, as well as various hybrid reticle types. One example of a programmable mirror array uses a matrix configuration of small mirrors, each of which can be individually tilted to reflect incident radiation beams in different directions; in this manner, the reflected beams are patterned . The support structure can hold the patterned device. The manner in which the support structure holds the patterned device may depend on the orientation of the patterned device, the design of the lithographic device, and other conditions (such as whether the patterned device is held in a vacuum environment). The support can use mechanical clamping, vacuum or other clamping techniques, such as electrostatic clamping under vacuum conditions. The support structure can be, for example, a frame or table that can be fixed or movable as desired, and which can ensure that the patterned device is, for example, in a desired position relative to the projection system. Any use of the terms "folder" or "reticle" herein is considered synonymous with the more general term "patterned device." The term "projection system" as used herein shall be interpreted broadly to encompass various types of projection systems suitable for, for example, exposure radiation used or other factors such as the use of infiltrating fluids or the use of vacuum, Including refractive optical systems, reflective optical systems, and catadioptric optical systems. Any use of the term "projection lens" herein is considered synonymous with the more general term "projection system." The term "illumination system" as used herein may also encompass various types of optical components for guiding, shaping or controlling a radiation beam, including refractive, reflective, and catadioptric optical components, and such components may also be collectively Ground or singularly referred to as a "lens." The lithography device can be of the type having two (dual stage) or more than two substrate stages (and/or two or more than two support structures). In such "multi-stage" machines, additional stations may be used in parallel, or preliminary steps may be performed on one or more stations while one or more other stations are used for exposure. The lithography apparatus can also be of the type wherein the substrate is immersed in a liquid (eg, water) having a relatively high refractive index to fill the space between the final element of the projection system and the substrate. Infiltration techniques are well known in the art for increasing the numerical aperture of a projection system. Figure 1 schematically depicts a lithography apparatus in accordance with a particular embodiment of the present invention. The apparatus comprises: - an illumination system (illuminator) IL for adjusting a radiation beam PB (eg, UV radiation or EUV radiation); - a support structure MT for supporting a patterned device (eg, a reticle) MA and Connected to a first positioning device PM for accurately positioning the patterned device relative to the projection system PL; - a substrate stage (eg, wafer table) WT for holding the substrate (eg, resist coating crystal Circle W, and connected to a second positioning device PW for accurately positioning the substrate relative to the projection system PL; - a projection system (eg, a refractive projection lens) PL configured to be imparted by the patterned device MA Patterning of the radiation beam PB onto the target portion C of the substrate W (eg, including one or more dies); and - a controller CN configured to control one or more components of the lithography device and/or Or calculate one or more attributes associated with the lithography apparatus. As depicted herein, the device is of the transmissive type (eg, using a transmissive reticle). Alternatively, the device may be of a reflective type (eg, using a programmable mirror array of the type mentioned above). The illumination system IL receives the radiation beam from the radiation source SO. For example, when the source is a quasi-molecular laser, the source and lithography devices can be separate entities. Under such conditions, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transmitted from the source SO to the illumination system IL by means of a beam delivery system BD comprising, for example, a suitable guiding mirror and/or beam expander. In other cases, the source can be an integral part of the device. The source SO and illumination system IL along with the beam delivery system BD (when needed) may be referred to as a radiation system. The illumination system IL may comprise an adjustment member AM for adjusting the angular intensity distribution of the beam. In general, at least the outer radial extent and/or the inner radial extent (commonly referred to as σ outer and σ inner, respectively) of the intensity distribution in the pupil plane of the illumination system can be adjusted. In addition, the illumination system IL typically includes various other components such as the concentrator IN and the concentrator CO. The illumination system provides a modulated radiation beam PB having a desired uniformity and intensity distribution in its cross section. The radiation beam PB is incident on a patterned device (e.g., reticle) MA that is held on the support structure MT. In the case where the patterned device MA has been traversed, the light beam PB is transmitted through the projection system PL, and the projection system PL focuses the light beam onto the target portion C of the substrate W. With the second positioning device PW and the position sensor IF (for example, an interference measuring device), the substrate table WT can be accurately moved, for example, to position the different target portions C in the path of the light beam PB. Similarly, the first positioning device PM and another position sensor (which is not explicitly depicted in Figure 1) can be used, for example, after mechanical extraction from the reticle library or during the scanning relative to the beam PB The path to accurately position the patterned device MA. In general, the movement of the object table MT and WT will be achieved by means of a long stroke module (rough positioning) and a short stroke module (fine positioning) forming part of the positioning means PM and PW. However, in the case of a stepper (relative to the scanner), the support structure MT may be connected only to the short-stroke actuator or may be fixed. The patterned device MA and the substrate W can be aligned using the patterned device alignment marks M1, M2 and the substrate alignment marks P1, P2. The device depicted can be used in the following preferred modes: 1. In the step mode, when the entire pattern to be imparted to the light beam PB is projected onto the target portion C at a time, the support structure MT and the substrate table WT are kept substantially Stationary (ie, a single static exposure). Next, the substrate stage WT is displaced in the X and/or Y direction so that different target portions C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C of the image in a single static exposure. 2. In the scan mode, when the pattern to be given to the light beam PB is projected onto the target portion C, the support structure MT and the substrate stage WT (i.e., single-shot dynamic exposure) are synchronously scanned. The speed and direction of the substrate stage WT relative to the support structure MT are determined by the magnification (reduction ratio) and image inversion characteristics of the projection system PL. In the scan mode, the maximum size of the exposure field limits the width of the target portion in a single dynamic exposure (in the non-scanning direction), and the length of the scanning motion determines the height of the target portion (in the scanning direction). 3. In another mode, the support structure MT is held substantially stationary while the pattern to be imparted to the beam PB is projected onto the target portion C, thereby holding the programmable patterning device and moving or scanning the substrate table WT . In this mode, a pulsed radiation source is typically used and the programmable patterning device is updated as needed between each movement of the substrate table WT or between successive pulses of radiation during the scan. This mode of operation can be readily applied to matte lithography utilizing a programmable patterning device such as a programmable mirror array of the type mentioned above. Combinations of the modes of use described above and/or variations or completely different modes of use may also be used. The radiation source SO can emit radiation exhibiting spatial coherence with coherence length and temporal coherence with coherence time. For example, in embodiments where the radiation source SO comprises a laser (e.g., a quasi-molecular laser), the emitted laser beam can exhibit spatial and temporal coherence. In the illumination system IL and/or the projection system PS, radiation from different portions of the radiation beam emitted from the radiation source SO may be mixed together. The spatial coherence of the radiation beam can cause different portions of the radiation beam to be mixed together to interfere with one another, thereby forming an interference pattern. In particular, an interference effect commonly referred to as a spot can occur. A spot is a change in the position of the intensity of a radiation beam caused by mutual interference of a set of wavefronts. For example, radiation in the image plane of the lithography device can interfere. Therefore, the interference pattern is formed in the image plane. The interference pattern may be referred to as a spot pattern. The substrate W is typically located substantially in the image plane of the lithography apparatus LA. Therefore, the spot pattern in the image plane will affect the spatial intensity profile of the substrate W to which it is exposed. During the lithography procedure, it is desirable to control the dose of radiation received at different locations on the substrate W. The received radiation dose at a given point on the substrate is the integral of the intensity of the radiation received over time at which exposure to radiation occurs. At a single point in time, different locations on the substrate W can receive radiation of different intensities due to static spots (instant spot patterns). However, the spot pattern can vary over time. The time scale over which the spot pattern changes is the coherence time of the radiation beam. If the area of the substrate is exposed to a time period (exposure time) where the radiation duration is much greater than the coherence time, the spot pattern will change multiple times during the exposure time. This situation can eliminate the effect of the spot pattern over time, and therefore, the spot can only cause a relatively small change in the dose of radiation received at different locations across the exposed area of the substrate W. However, if the exposure time is on the order of magnitude equal to the coherence time or the exposure time is less than the coherence time, the spot pattern may not change during the exposure time or may only change a few times. Thus, different portions of the exposed area of substrate W can receive different doses of radiation due to the spot. In embodiments where the radiation source SO provides a pulsed radiation beam, the coherence time of the radiation beam can be less than the duration of a single pulse of the radiation beam. Thus, more than one spot pattern can occur during a single pulse of the radiation beam. In some embodiments, the exposure period can include multiple pulses of the radiation beam. This can be used to increase the total number of spot patterns to which a given point on the substrate is exposed, thereby averaging the effect of the spot seen during a single exposure period over time. In some embodiments, a single pulse of radiation can include a plurality of individual spot patterns. For example, the number of independent spot patterns in a single pulse of radiation can be greater than ten. In some embodiments, the number of individual spot patterns in a single pulse of radiation can be about 25, about 50, or about 100 or more. Reference herein to "exposure time" is intended to mean the total amount of time that a given point on a substrate is exposed to radiation. In an embodiment using a pulsed radiation source, the exposure time is equal to the integral of all pulses of the radiation to which a given point on the substrate is exposed. The exposure time does not include the time between the radiation pulses. Reference herein to "exposure period" is intended to mean the period of time during which radiation (e.g., a pulse of radiation) is received by a given point on a substrate. The exposure period can, for example, include a plurality of radiation pulses and include a time period between the radiation pulses. The change in position of the radiation dose across the substrate W can affect the features that are patterned onto the substrate W. For example, the substrate W may be provided with a resist layer (for example, using a tool called a coating development system). The area of the resist is exposed to radiation during the lithographic exposure, thereby causing a change in state of the resist in the exposed regions. The resist can then be developed by performing an etching process to remove the exposed regions of the resist that have undergone a state change or a non-exposed region of the resist that has not undergone a state change. Etching of some of the resist regions results in the features being patterned into the resist. The patterned features in the resist can form a reticle for patterning features into the substrate W, for example, by etching portions of the substrate W from which the resist has been removed. The size of the features patterned into the resist and subsequently patterned into the substrate W depends on the dose of radiation received by the resist (at the substrate W). For example, in some embodiments, one or more line features can be patterned into a resist and subsequently patterned onto the substrate W. Line feature width W_L It depends on the dose of radiation received at the substrate W. The width of the lithography feature W_L It is alternatively referred to as the critical dimension (CD) of the lithography feature. In general, two different types of resists can be used to form a pattern on the substrate W. The two different types of resists may be referred to as positive-tune resists and negative-tune resists. The negatively tuned resist is configured to undergo a state change upon exposure to radiation such that the exposed portion of the resist is resistant to being etched away during the etching process and thus remains on the substrate W. Portions of the resist that are not exposed to radiation are etched away during the etching process. When a negative-tune resist is used, the increase in the dose received at the substrate will increase the width of the line feature._L And the reduction in the received dose will reduce the width of the line feature W_L . The positive tone resist is configured to undergo a state change upon exposure to radiation such that the exposed portion of the resist is etched away during the etching process and is thus removed from the substrate W. Portions of the resist that are not exposed to radiation are resistant to being etched away and thus remain on the substrate W. Thus, during the etching process, portions of the resist that are exposed to radiation are etched away during the etching process. When a positive-tune resist is used, the increase in the dose received at the substrate W will reduce the line width W_L And the reduction in the received dose will increase the width of the line feature W_L . The methods described herein seek to determine the dose of radiation received at substrate W that varies according to the location on substrate W. This can be achieved by using a positive-tune resist or a negative-tune resist, since the line width W is used when two forms of resist are used._L Depending on the dose of radiation received. Therefore, the line width W depending on the position of the line feature by the exposure line feature_L The measurement can be used to determine the dose of radiation received at each location along the line feature. As will be appreciated from the above description, variations in the received radiation dose at different locations on the substrate W (e.g., caused by spots) can cause different doses of radiation to be received at different locations along the line features. Variations in the received dose along the line feature can result in variations in the width of the line features at different locations along the line. The change in width of the line feature along the length of the line can be referred to as line width roughness. Line width roughness is a common measure used to characterize lithography features. As explained above, the interference effect (especially the spot) in the lithography apparatus LA can affect the line width roughness of the lithographic features formed by the lithography apparatus LA. Increasingly, it is required to reduce the size of the lithographic features (often referred to as critical dimensions). As the critical dimension decreases, the effect of linewidth roughness becomes an increasingly important factor and the contribution to linewidth roughness needs to be understood and quantified. In general, there may be many different effects that contribute to line width roughness, and it is difficult to separate such effects. In particular, it is difficult to assess the contribution of the spot to line width roughness as it also contributes to the many random effects of line width roughness. Other random effects that contribute to line width roughness can, for example, include effects on chemical procedures that occur in the resist used during lithographic exposure. For some uses of the lithography apparatus LA, it may be desirable to reduce the bandwidth of the radiation provided by the radiation source SO and/or reduce the number of pulses of radiation emitted from the radiation source SO during a single exposure period. Reducing the bandwidth of the radiation typically increases the coherence length and coherence time associated with the radiation, and thus increases the dose variation caused by the spot (the coherence time is equal to the coherence length divided by the speed of light). Reducing the number of radiation pulses during the exposure period will reduce the total exposure time for exposing a given point on substrate W to radiation. This situation will reduce the number of independent spot patterns seen by a given point on the substrate, and thus, the effect of the spot on the dose of radiation received at that point on the substrate can be increased (assuming the coherence time remains the same). Therefore, the contribution of the spot to the line width roughness can be particularly important in the case where the expected bandwidth and/or the number of pulses is reduced. In general, it is necessary to determine the effect of the flare in the lithography apparatus. For example, it may be desirable to determine the contribution of the spot to changes in the lithographic features formed in the substrate W by the lithography apparatus LA. For example, it may be desirable to determine the contribution of the spot to the line width roughness of the line features formed in the substrate W by the lithography apparatus LA. Advantageously, determining the effect of the spot in the lithography apparatus LA allows for a better understanding of the effect of the spot and allows for proper consideration of the spot when selecting other attributes of the lithographic apparatus LA. For example, advantageously, the understanding of the spot effect may allow for selection of the bandwidth and/or number of pulses (during the exposure period) of the radiation emitted from the radiation source SO while considering the effect of the spot. Frequently used spot contrastC To quantify the spot. Spot contrastC Is defined as the standard deviation σ of the radiation intensity across a region divided by the average radiation intensity across the regionAnd can be given by equation (1).(1) where N is the number of independent spot patterns that are exposed to a given point during a single exposure period. In embodiments where the radiating element SO comprises a laser that emits a laser beam, the number N of independent spot patterns is equal to the number of independent laser modes that the laser is operating during a given exposure period. The contribution of the spot to line width roughness depends on the spot contrast. As mentioned above, determining the contribution of the spot to variations in lithographic features (e.g., line width roughness) is complicated by the presence of other contributions (such as random effects) that also cause changes in the lithographic features. Embodiments of the invention contemplated herein seek to limit the contribution of light spots to other effects by limiting the effect of the spot to the finite spatial frequency in the image plane of the lithography apparatus LA (the plane of the substrate to be exposed is substantially in the plane). Separation. Signal processing analysis can be used to analyze different spatial frequencies in the image plane of the lithography apparatus. One or more of the lithographic features that vary by location can be viewed as a series of different contributions at different spatial frequencies. For example, the line width of the line feature at different locations along a line of features_L Can be considered as a sequence. 2 is an image of the lithographic features 11a, 11b formed in the substrate W. The image shown in Figure 2 was acquired using a scanning electron microscope. The edges of the first crepe feature 11a and the second tilogram feature 11b have been detected and marked with the solid lines in FIG. Appropriate image processing techniques can be used to detect the edges of lithographic features, such as tiling lines 11a, 11b. Once the edges of the reticle 11a, 11b are detected, the distance between the detected edges can be determined. The distance between the detected edges is the line width and is labeled W in Figure 2._L . As can be seen in Figure 2, the line width of the immersion feature W_L It varies depending on the position along the x-axis. The x-axis extends substantially parallel to the direction in which the immersion lines extend. Line width W of each line 11a, 11b at different x positions_L Form a series with different contributions at different spatial frequencies. Figure 3 is a plurality of line widths W according to spatial frequency (in micrometers)_L A representation of the average power spectral density of the series. The representation shown in Figure 3 shows the line widths at different x positions at different spatial frequencies._L The contribution of the formed line width series. Line width W_L The power spectral density of the series includes contributions from the spot and contributions from effects other than the spot. Embodiments of the invention contemplated herein seek to separate the contribution caused by the spot with other contributions to derive the changes caused by the spot. Figure 4 is a representation of the autocorrelation function (expressed as a percentage) of the series of line widths as a function of positional offset (in microns). The autocorrelation function is a measure of the similarity between the two series. In the situation shown in Figure 4, the first line width series is compared to the same second series. The first series and the second series are offset from each other by different distances, and the autocorrelation between the two series is calculated at each offset. Figure 4 shows the calculated autocorrelation function at different position offsets between the first series and the second series. A large center maximum 13 is seen around the offset of 0 microns in Figure 4. This center maximum 13 indicates that the first series is the same as the second series (this is due to the absence of an offset between them) and thus the series is highly correlated. The height of the center maximum 13 is equal to the total variance of the series of line widths (the square of the standard deviation σ). On either side of the center maximum 13, a first local maximum 15a and a second local maximum 15b can be seen. The first local maximum 15a and the second local maximum 15b represent positional offsets (compared to other ambient offsets) that have an increased correlation between the first series and the second series. The power spectral density of the linewidth series at different frequencies (as shown in Figure 3) and/or the autocorrelation of the linewidth series at different offsets (as shown in Figure 4) may be used in some embodiments. Analyze linewidth series at one or more spatial frequencies. If the contribution of the spot is limited to a finite spatial frequency, tools such as power spectral density and/or autocorrelation function can be used to separate the effect of the spot from other random effects. There is a Fourier relationship between the autocorrelation of the spot contrast in the image plane of the optical system and the intensity profile of the radiation in the illumination pupil of the optical system. This Fourier relationship can be used to limit the contribution of the spot in the image plane to a limited spatial frequency. For example, if the radiation in the illumination pupil has a periodic intensity profile, this is used to limit the contribution of the spot in the image plane to the limited spatial frequency determined by the period of the intensity profile in the illumination pupil. Figure 5 is a schematic representation of the intensity profile of radiation in an illumination pupil of a lithography system. The bright shading in Figure 5 indicates high intensity and the dark shading indicates low intensity. The illumination pupil is a pupil plane that determines the illumination of the patterned device MA located in the plane of the object. The illumination pupil has a Fourier relationship with the plane of the object in which the patterned device MA is located. That is, the spatial intensity profile of the radiation in the illumination pupil determines the angular intensity profile of the radiation in the plane of the object. The illumination system IL is operable to control the spatial intensity profile in the illumination pupil, thereby controlling the angular intensity profile utilized by the illumination patterning device MA. For example, during typical lithography exposure, illumination system IL can be configured to limit the spatial extent of the radiation in the illumination pupil to a plurality of polar regions (eg, dipole or quadrupole configurations) to form a multi-pole illumination mode. The multi-pole illumination mode illuminates the patterned device MA from one or more discrete angular ranges. The illumination pupil shown in Figure 5 has a periodic intensity profile in the x direction as indicated in Figure 5. In the embodiment shown in Figure 5, the intensity is a sinusoidal function of the position on the x-axis. The sine function has a period P_p . The sinusoidal function can be, for example, a cosine function such that the intensity of the radiation at the center x position (in Figure 5, x = 0) in the illumination pupil is substantially a local maximum or a local minimum. It should be understood that the intensity of the radiation may not be negative at any location in the illumination pupil. In practice, the intensity of the radiation that varies according to the x position in the illumination pupil can be proportional to 1+cos(x). This intensity distribution is considered to be an example of a sine function and an example of a cosine function. The intensity that varies according to the position on the y-axis follows the center y position y_c (y = 0 in Fig. 5) is the center of the Gaussian distribution. Using a Gaussian distribution in the y-direction limits the range of y of the radiation in the illumination pupil to the central region of the y-domain. The y-direction as used herein refers to the scanning direction in which the substrate W and/or the patterned device MA are scanned relative to each other. The x direction used herein means a non-scanning direction perpendicular to the scanning direction. For the purposes of the methods described herein, it is desirable to have an isotropic behavior occurring at the substrate W. The isocentric behavior means that the line width W attributed to the focus change across the image plane is not introduced._L Variety. Therefore, the line width W_L The change can be uniquely attributed to a change in dose and is not caused by a change in focus. This situation allows the measurement line width W_L Change and use line width W_L Change to determine dose change. The isocentric behavior can be achieved by centering the radiation range defined in the y direction (in the illumination pupil) and centering the intensity profile of the radiation in the y direction around the center y position. However, if the radiation range in the y direction is too small, this can result in a high value of the local radiation intensity in the illumination system IL, which can damage the components of the illumination system IL. Thus, the range of radiation in the y-direction can be about 3% or greater of the y range of the illumination pupil. Although the range of radiation in the y-direction is limited to the central region of the illumination pupil, one or more diffraction orders may be formed as the radiation passes through the patterned device MA. For example, the radiation can pass through the line features of the patterned device MA and form a -1, 0, and +1 diffraction order (and can form a higher order diffraction order). In the pupil plane of the projection system PL, the diffraction orders may be distributed in the y-direction such that the range of radiation in the y-direction is no longer limited to the central y-region and includes positioning on either side of the central y-region +1 and -1 diffraction steps. In order to maintain the isocentric behavior, it may be desirable to limit the diffraction order passed through the projection system PL to the +1, 0, and -1 diffraction orders. This can be achieved, for example, by selecting the distance between the features on the patterned device MA relative to the numerical aperture NA of the projection system PL. The distance between features on the patterned device MA can be, for example, greater than λ/NA and can be less than 2λ/NA, where λ is the wavelength of the radiation. It may be further desirable to select a functional interval cycle of features on the patterned device MA to maintain a constant focus behavior at low exposure doses. The patterned device MA can, for example, include features having a spacing of approximately 160 nanometers. The wavelength λ of the radiation can be approximately 193 nm, and the numerical aperture NA of the projection system can be approximately 1.35. In this embodiment, the distance between approximately 160 nm is greater than λ/NA and less than 2λ/NA. In one embodiment, each pitch may, for example, comprise a transmission region having a width of approximately 120 nanometers and an attenuation region having a width of approximately 40 nanometers. This situation provides an action interval cycle that maintains a constant focus behavior at low exposure doses. In an alternate embodiment, the patterned device MA can, for example, comprise an alternating phase shift mask configured to provide a higher contrast than the patterned device described above. In an embodiment, the alternating phase shifting reticle may comprise a grating having a pitch of approximately 160 nanometers. The wavelength λ of the radiation can be approximately 193 nm, and the numerical aperture NA of the projection system can be approximately 1.35. One cycle of the alternating phase shift mask may include a first attenuation portion having a width of 40 nm, a first transparent portion having a width of 40 nm, a second attenuation portion having a width of 40 nm, and a width of 40 nm. Two transparent parts. The second transparent portion can be configured to apply a phase shift of 180° to the incident radiation, and the first transparent portion can be configured to not apply a phase shift. This alternating phase shift configuration is used to attenuate the radiation in the zero diffraction order, and in this case increases the contrast of the image formed on the substrate W (the radiation in a diffraction order is not attenuated). The attenuation of the zero-wrap order can substantially eliminate the zero-wrap order because the average E-field of the radiation in the other order is zero. In addition to increasing the contrast of the image formed at the substrate, eliminating the zero-wrap order will also advantageously halve the distance between the raster images formed at the substrate. In an alternate embodiment, the patterning device (NA) can, for example, comprise a grating that is formed as an alternating phase shifting mask that does not include an attenuating portion (ie, the reticle feature includes the entire region in which the relative phase shift is applied). The intensity profile of the illumination pupil shown in Figure 5 is periodic in the x-direction and is used to expose line features that extend in the x-direction. In an alternate embodiment, line features extending in the y-direction can be exposed. In such embodiments, the illumination pupil may be periodic in the y-direction (relative to the x-direction (as shown in Figure 5)). The intensity in the x direction may follow a Gaussian distribution centered at the center x position. The intensity profile in the illumination pupil can be established by controlling the illumination system IL. The illumination system IL can, for example, comprise a mirror array of adjustable orientations. Each of the mirror faces of the mirror array can receive a portion of the radiation beam provided by the radiation source SO and can direct the received portion of the radiation beam according to the orientation of the mirror. The orientation of the mirror can be configured to form a desired spatial intensity profile in the illumination pupil. For example, the orientation of the mirrors can be configured to form the spatial intensity profile shown in FIG. In the embodiment shown in Figure 5, the illumination pupil comprises 9 cycles P in the x direction_p . In other embodiments, the illumination pupil may include more or less than 9 cycles in the x direction._p . It may be desirable to have the illumination pupil include an integer number of cycles in the x direction._p . In some embodiments, the illumination system IL can be defined to form a symmetric spatial intensity profile in the illumination pupil. For example, the illumination system IL can form a spatial intensity profile that exhibits reflection symmetry around the center x position and/or reflection symmetry around the center y position. The symmetry of the illumination pupil can be a possible number of periods P in the x direction_p Limited to an odd number of cycles. In general, the spatial intensity distribution in the illumination pupil can include a totalK Cycles. In some embodiments,K Is an integer. In some embodiments,K It is odd. Number of periods in the illumination pupilK Can be greater than 2. In some embodiments, the number of periods in the illumination pupilK Can be 5 or more. In some embodiments, the number of periods in the illumination pupilK Can be 17 or less. As described above, a periodic spatial intensity profile (shown in Figure 5) in the illumination pupil is provided to limit the effect of the spot on the limited spatial frequency in the image plane in which the substrate W is located. The spatial frequency at which the visible light spot effect is located in the image plane (where the substrate W is located) has a period P_s . The period P of the visible spot effect_s Equation (2) is related to the periodicity of the spatial intensity profile in the illumination pupil.(2) where λ is the wavelength of the radiation beam provided by the radiation source SO, and NA is the numerical aperture of the projection system PL andK For the period P in the illumination pupil_p The number (as described above). 6 is a schematic representation of an autocorrelation function associated with a series of linewidths caused by exposure of lithographic features using periodic illumination pupils (eg, the illumination pupil shown in FIG. 5). As explained above with reference to Figure 4, the autocorrelation function includes a large center maximum 13 centered at a positional displacement of zero due to the high correlation between the same series (no displacement between the series). The first local maximum 15a and the second local maximum 15b are on either side of the central maximum 13. The first local maximum 15a and the second local maximum 15b are at a distance P from either side of 0 (the center maximum 13 is centered at the 0)_s And indicates that the line width series is offset from itself by the distance P_s The correlation of the increase in time. The correlation shown by the increase in the first local maximum 15a and the second local maximum 15b isK Cycles of periodic illumination are limited to 1/P_s The effect of the spot on the limited spatial frequency centered at the frequency. Thus, the first local maximum 15a and the second local maximum 15b provide a measure of the spot at the substrate W. For example, the height of the first local maximum 15a and the second local maximum 15bH _L It can indicate the contribution of the spot to the line width roughness. At 1/P_s The contribution of the spot at the spatial frequency will also be seen in the representation of the power spectral density of the linewidth series (not shown) depending on the frequency. The effect of the spot will causel /P_s The local maximum of the power spectral density at the spatial frequency, wherel Is a positive integer andl ≤ K. Figure 7 is a representation of an autocorrelation function associated with a number of different line width series. The different line width series shown in Figure 7 represents the line width caused by exposure of line features using different illumination pupils. The first curve 101 shown in Figure 7 represents a reference exposure using an illumination pupil that is not periodic. The second curve 103 indicates that there are 5 cycles in the illumination pupil (K =5) Execution exposure. The third curve 105 indicates that there are 9 cycles in the illumination pupil (K =9) Execution exposure. The fourth curve 107 indicates that there are 13 cycles in the illumination pupil (K =13) Execution exposure. The fifth curve 109 indicates that there are 17 cycles in the illumination pupil (K =17) Execution exposure. Each of the autocorrelation functions shown in Figure 7 exhibits a second local maximum 15b. The autocorrelation function also exhibits a first local maximum, however, such first local maximums are not shown in FIG. As can be seen in Figure 7, the location and height of the local maximum 15b are different for different illumination pupils. As explained above, the position of the local maximum is the period P of the visible spot effect._s . Period P_s It is given by equation (2) above and depends on the number of periods in the illumination pupilK . Therefore, for the different number of periods in the illumination pupil as seen in Figure 7K The location of the local maximum 15b is different. Figure 8 shows the different numbers of cycles in the use of illumination pupils.K The representation of the position of the different local maximum 15b observed. The position of the local maximum 15b is equivalent to the period P of the visible spot effect_s . The data shown in Figure 8 is by using different numbers of periods in the illumination pupilK Obtained by exposing several different line features. The line features in the substrate W are observed using a scanning electron microscope to produce an image of the line features. The images are analyzed to detect edges of the line features to determine the line width W at different locations along the line._L . Line width W at different locations along the line_L Used to construct a line width series. For a given number in the illumination pupilK Each illumination mode of the cycle can expose a plurality of different line features and can derive a line width W from each of the exposed line features_L series. For example, in some embodiments, more than about 100 line features can be exposed for a given illumination mode, thereby providing more than about 100 line width series. In some embodiments, more than about 1000 line features can be exposed for a given illumination mode to provide more than about 1000 line width series. A plurality of line width series for a given illumination mode can be used to calculate an average power spectral density for the given illumination mode. Used for numberK The average power spectral density of each illumination mode of the period is used to calculate for each numberK The autocorrelation function of the period. The autocorrelation function is calculated at different position offsets and the location of the local maximum is determined, thereby providing the information shown in FIG. As can be seen in Figure 8, the location of the local maximum and the period as predicted by equation (2)K The number increases proportionally. Figure 9 is forK A representation of the height of the local maximum 15b of different values. As can be seen from Figure 9,K The different values of the local maximum 15b are different. This change in the height of the local maximum 15b is mainly attributed toK The difference in lighting patterns at different values. A certain change in the height of the local maximum 15b shown in Fig. 9 can also be attributed to a small difference in experimental conditions when exposure is performed. The autocorrelation function contains contributions from the spot and contributions from other random effects (eg, the results of chemical procedures that occur in the resist used during the exposure process). As described above, advantageously, by using a periodic illumination mode, the effect of the spot is limited to a limited number of spatial frequencies. Therefore, the height of the local maximum 15b in the autocorrelation function is mainly attributed to the contribution of the spot. The height of the local maximum 15b therefore depends, at least in part, on the spot contribution and can be used to determine the contribution of the spot to the line width roughness. However, the height of the local maximum 15b also includes some contribution from other random effects. It is necessary to separate the contribution of the spot from other contributions. The contribution of the spot can be separated from other contributions by deriving a reference autocorrelation function that refers to the use of a non-periodic illumination mode (such as the first curve 101 shown in Figure 7). For example, an illumination pattern that includes an intensity profile that is not periodic in the pupil plane can be used to expose one or more line features. An autocorrelation function corresponding to the exposed line feature can be calculated and this autocorrelation function can serve as a reference autocorrelation function. The reference autocorrelation function will include contributions from the spot, but these contributions are spread across all spatial frequencies (this is due to the use of non-periodic illumination modes). Therefore, the height of the reference autocorrelation function at each position offset will be primarily due to contributions other than the spot and does not depend on the illumination mode used. The reference autocorrelation function can be subtracted from the autocorrelation function derived using the periodic illumination mode to separate the effect of the spot from other contributions. For example, the difference between the height of the local maximum 15b in the autocorrelation function derived using the periodic illumination mode and the height of the reference autocorrelation function at the same position offset can be determined. The resulting difference is a measure of the contribution of the spot to line width roughness (where other contributions are subtracted) in the case of using a particular illumination mode. The determined height of the local maximum 15b in the autocorrelation function can be expressed as H_L . The height of the reference autocorrelation function at a position offset corresponding to the local maximum 15b in the autocorrelation function derived using the periodic illumination mode may be referred to as the reference local maximum height and may be represented as H_LR . Determined height H_L With reference height H_LR The difference between the two can be called the maximum height of the spot and can be expressed as H_LS , where H_LS =H_L -H_LR . In some embodiments, the reference autocorrelation function (including the reference local maximum height H) may be derived by means other than performing exposure using a non-periodic illumination mode._LR ). For example, in some embodiments, the autocorrelation function that can be determined from using the periodic illumination mode estimates the reference self by considering an autocorrelation function at a position offset on either side of the local maximum 15b. related functions. That is, the height of the autocorrelation function on either side of the local maximum 15b can be used to estimate the autocorrelation function H that would occur if there is no local maximum (corresponding to the condition using the aperiodic illumination mode)_LR The height (under the position offset corresponding to the local maximum). Methods for deriving the contribution of a spot when using a particular illumination mode have been described above. For example, the maximum height of the spot local area H_LS Provides a measure of the contribution of the spot. However, this measure is dependent on the illumination mode used to form the autocorrelation function and may be different for different illumination modes. It may be desirable to provide a measure of the spot contribution that is independent of the illumination mode used during the measurement procedure. This measure can then be used to estimate the contribution of the spot when performing exposure using an illumination mode that is different from the illumination mode used during the measurement procedure. For example, during a typical lithography exposure procedure, a multi-pole illumination mode (eg, a dipole illumination mode) may be required. The multi-pole illumination mode differs from the periodic illumination mode that can be used to measure the contribution of the spot. Therefore, there is a need to provide a measure of the contribution of the spot associated with all lighting modes. A measure of the contribution of the spot that is independent of the illumination mode used may, for example, include the line width W caused by the spot._L The variance (or equivalently, the standard deviation σ). In some embodiments, the measure of spot contribution independent of the illumination mode used may include the variance (or equivalently, standard deviation σ) of the radiation dose caused by the spot. In some embodiments, the measure of spot contribution independent of the illumination mode used may, for example, include spot contrastC . Equivalently, the measure of spot contribution independent of the illumination mode used may include the number of independent spot patterns exposed to a given point on the substrate during a single exposure period.N . As explained above, in embodiments where the radiation source SO comprises a laser (e.g., a quasi-molecular laser), the number of individual spot patternsN Equal to the number of independent laser modes in the excitation of the laser during the exposure period. As mentioned above, the height of the center maximum 13 of the autocorrelation function is equal to the total variance of the series of line widths (the square of the standard deviation σ). It may be desirable to determine the variance (or equivalently, standard deviation σ) of the series of line widths attributed to the spot. That is, it may be necessary to determine the height of the center maximum (i.e., the total variance) that would be caused if the only contributor of the other party's difference is the spot. In the case of the measurement procedure described above, the height of the resulting center maximum 13 (i.e., the total variance) will include other contributions as well as contributions from the spot. Therefore, the height determination of the resulting center maximum value 13 using the above measurement program does not directly contribute to the contribution of the spot difference. In some embodiments, the height of the local maximum 15b can be used to estimate the height of the central maximum 13 in the autocorrelation function corresponding to the change caused only by the spot. That is, the height of the local maximum 15b can be used to estimate the total variance due to the spot. An autocorrelation function corresponding to a change caused only by a spot may be referred to as a spot autocorrelation function. As explained above, after subtracting the reference autocorrelation function, the height of the local maximum 15b in the autocorrelation function (called the spot height maximum height H)_LS ) can be considered to be due only to the effect of the flare and not to any other contribution. Therefore, the maximum local height of the spot is H_LS Can be considered as the point on the spot autocorrelation function. If the general shape of the spot autocorrelation function is known, then the determination of a point on the spot autocorrelation function can be used to determine other points on the spot autocorrelation function. In detail, if the ratio between the local maximum 15b and the central maximum 13 in the spot autocorrelation function is known, the maximum local height H of the spot is_LS The determination can be used to determine the height of the center maximum in the spot autocorrelation function. The height of the central maximum 13 in the spot autocorrelation function can be referred to as the maximum height of the spot center and can be expressed as H._CS . As explained above, it may be necessary to determine the maximum height of the spot center H_CS Maximum height H with spot local area_LS Ratio between R_S , as given by equation (3).(3) The ratio R_S Available from the maximum height of the spot area H_LS The value determined experimentally determines the maximum height of the spot center H_CS . The ratio R_S It can depend on the lighting mode used. Therefore, it may be necessary to perform the local maximum height H of the spot._LS The same illumination mode determination ratio R_S . In some embodiments, the ratio R can be determined via the measurement of the intensity profile of the illumination pupil._S . For example, the intensity profile of the illumination pupil can be determined by measuring the angular intensity profile of the radiation received at the image plane of the projection system PL. For example, a patterned device MA comprising a small pinhole aperture can be positioned in the plane of the object such that radiation is only transmitted through a small extent of the plane of the object. The aperture in the patterned device MA receives radiation having an angular distribution that depends on the illumination pupil being used. Radiation propagates through the aperture and through the projection system PL and onto the image plane (the plane on which the substrate W is positioned during lithographic exposure). One or more image sensors can be used to measure the angular intensity profile of the radiation in the image plane. For example, a wavefront sensor can be used to derive an angular intensity profile of the radiation in the image plane. A wavefront sensor that can be used to derive an angular intensity profile of the radiation in the image plane can already be present in the lithography apparatus and is operable to measure the wavefront aberration caused by the projection system PL. The angular intensity profile in the image plane is equivalent to the spatial intensity profile in the illumination pupil. The Fourier transform of the spatial intensity profile (or equivalently, the angular intensity distribution in the image plane) in the illumination pupil can be determined. The Fourier transform of the spatial intensity profile of the illumination pupil is equivalent to the autocorrelation function of the intensity profile in the field or image plane (eg, the image plane in which the substrate W is located). Therefore, the Fourier transform of the spatial intensity profile of the illumination pupil can be referred to as the autocorrelation function of the illumination pupil. Figure 10 is a representation of the autocorrelation function of the measured intensity in an illumination pupil at different position offsets. The autocorrelation function shown in Figure 10 is calculated by measuring the intensity in the illumination pupil at different locations. At each x position, the radiant intensities across all y positions can be summed to provide a sum of the radiant intensities at a given x position. Summing the radiant intensity throughout y at different x positions provides a series of intensity measurements at different x positions. This series of Fourier transforms can be performed to determine the autocorrelation function shown in FIG. The autocorrelation function shown in Figure 10 is shown as a percentage of the height of the center maximum (not shown in Figure 10) in the autocorrelation function. As can be seen in Figure 10, a local maximum 15b appears in the autocorrelation function. The local maximum 15b is in a period P equivalent to the periodic intensity profile in the illumination pupil_p The position and height is approximately 25% of the height of the center maximum in the autocorrelation function. The ratio between the maximum height of the center and the maximum height of the local area can be approximately the same for the autocorrelation function of the intensity profile of the illumination pupil, just as for the spot autocorrelation function. Therefore, the ratio between the center maximum height and the local maximum height can be determined from the autocorrelation function of the intensity profile of the illumination pupil and can be used as the ratio R given by equation (3)._S Estimate. Estimated ratio R_S Can be used to recombine equation (3) from the local maximum height of the spot H_LS Determine the maximum height of the spot center H_CS . Figure 11 is for the number of cycles in the illumination pupilK The representation of the height of the local maximum 15b in the autocorrelation function of the illumination pupil of the different illumination modes of different values (as a percentage of the height of the central maximum in the autocorrelation function). The height of the local maximum as shown in Figure 11 and expressed as a percentage may provide for a number of different number of periods in the illumination pupilK Ratio R_S (as expressed by equation (3)). Using the above procedure, it is possible to derive the contribution of the spot to the variance of the line width roughness. For example, in a particular experiment, there are 17 cycles in the illumination pupil (ie,K The illumination mode of =17) is used to expose several line features. The measured line width at different locations along the exposed line features is used to determine an autocorrelation function similar to the autocorrelation function shown in FIG. It is derived that the height of the central maximum 13 in the autocorrelation function associated with the series of measured line widths is approximately 3.68 square nanometers. As described above, the height of the center maximum 13 in the autocorrelation function is equal to the total variance of the line widths (including contributions from spots and other effects). The corresponding standard deviation σ (the square root of the variance) is approximately 1.92 nm. As can be seen from Figure 7,K The height of the local maximum in the autocorrelation function associated with the value of = 17 is considered to be approximately equal to 0.12 square nanometer. Figure 11 shows atK At a value of =17, the height of the local maximum of the autocorrelation function associated with the illumination pupil is approximately 20%. Therefore,K The maximum height of the spot center of the value of =17_CS Maximum height H with spot local area_LS Ratio between R_S It is approximately 0.2. By recombining equation (3), the maximum height of the spot center H_CS H_LS /R_S =0.12/0.2=0.6 nm² Given. As explained above, the maximum local height of the spot is H_LS The variance of the line width caused by the spot. Therefore, the variance caused by the spot is estimated to be 0.6 square nanometers. The corresponding standard deviation σ of the line width caused by the spot is=0.77 nm is given. The change in line width caused by the spot can be used to determine the change in dose caused by the spot. As explained above, the linewidth of the features depends on the dose of radiation received. Therefore, the variation in the line width of the feature depends on the dose change of the received radiation. The relationship between the radiation dose and the line width depends on the illumination pupil used and can be determined by separation experiments. For example, an experiment can be performed that exposes several different line features using a given illumination mode. The dose to which the substrate is exposed to radiation can be varied and the resulting change in line width can be measured. These measurements can be used to derive the sensitivity of line width to dose variation for a particular illumination mode. The same procedure can be performed using several different illumination modes to derive the sensitivity of line width to dose variation for each illumination mode. The sensitivity of line width to dose variation for a given illumination mode can be used to convert line width variations into dose changes. For example, a lookup table for sensitivity of line width to dose change for different illumination modes can be stored. The lookup table can be referenced and the lookup table can be used to convert the measured line width variation into a dose change. The change in line width caused by the spot can depend on the lighting mode used. However, the dose change caused by the spot can be independent of the illumination mode used. Thus, the dose change caused by the spot can be a measure of the amount of light that provides information about the contribution of the spot in the case of any illumination mode. Using the method described above, in a particular experiment, it was determined that the standard deviation σ of 0.77 nm from the line width caused by the spot corresponds to a dose change of approximately 0.64% along the line characteristic due to the spot. As explained above, this dose change is independent of the illumination mode. The measurement of the spatial intensity profile of the self-illuminating pupil has been described above to estimate the maximum height H of the spot center._CS Maximum height H with spot local area_LS Ratio between R_S The method. In other embodiments, other means may be used to estimate the ratio R_S . For example, in some embodiments, a simulation can be used to estimate the ratio R_S . For example, a simulation of the radiation propagating through the projection system PL can be performed to derive an analog spot pattern. The autocorrelation function can be derived from the simulated spot pattern. The height of the central maximum in the simulated autocorrelation function and the height of the local maximum can be used to determine the ratio of the height of the local maximum to the height of the central maximum._S . Ratio R derived via simulation_S Can be used to determine the maximum height of the spot area from the experiment_LS Determine the maximum height of the spot center H_CS . An example of a simulation that can be used to determine the simulated spot pattern can be a Monte Carlo simulation. For example, a coherent Monte Carlo simulation can be used to simulate the propagation of radiation through a lithography device. The input to the simulation can include a plurality of radiation sources in a plane. Each radiation source can have the same intensity and the relative phase of each source can be modeled as random. The effects of the illumination system IL, the patterned device MA, and the projection system PL can be simulated by an amplitude filter. At each location in the image plane of the projection system, the intensity from each source can be summed to define the intensity at that location. Therefore, the output of the simulation can be the intensity distribution of the radiation in the image plane. The output intensity distribution can be used to derive the available export ratio R_S Autocorrelation function. In some embodiments, a classic simulation of a partially coherent radiation source can be performed. This simulation can be used to output the optical transfer function of the lithography device. The optical transfer function is equivalent to the power spectral density at which the autocorrelation function can be derived. Autocorrelation function can be used to determine the ratio R_S . The simulation of the partially coherent radiation source can include modeling the intensity distribution in the illumination pupil into a series of incoherent point radiation sources. The simulated point source can, for example, be configured to mimic a periodic illumination mode as described above (eg, the periodic illumination mode depicted in FIG. 5). The envelope of the point source distribution in the illumination pupil is matched to the illumination pupil fill. The propagation of radiation from each point source is simulated by the patterning device MA and the projection system to provide a simulation of the radiation incident on the image plane of the projection system in which the substrate W is located. The patterned device MA can be modeled as a periodic series of transmission lines (eg, lines extending in the non-scanning direction). For example, the patterned device MA can be modeled as having a periodic line pattern that is approximately 160 nanometers in period. At the patterned device MA, the radiation from each point source in the illumination pupil is translated into a plane wave propagating in a given direction. The patterned device MA is used to diffract the simulated plane wave into a plurality of beams. In the projection system PL, the diffraction pattern can be truncated by the finite numerical aperture NA of the projection system PL. In the image plane of the projection system, the intensity profile resulting from each point source in the illumination pupil is determined. The summation of the intensity profiles in the image plane resulting from each point source is then performed to derive the total intensity profile in the image plane. The summation of contributions from each point source is performed as a non-coherent sum. The propagation of the radiation is performed by the simulation of the lithography apparatus as a coherent sum (ie, the sum of the amplitudes). In some embodiments, other factors can be considered in the simulation. For example, the propagation of radiation can be simulated into a resist located in the image plane and/or subsequent development of the resist. In some embodiments, the effect of the polarization of the radiation can be considered in the simulation. For example, the polarization effects in the illumination pupil, at the patterned device MA, and in the image plane can be considered in the simulation. In some embodiments, the simulation may additionally consider, for example, the three-dimensional imaging effects at the patterned device MA and at the substrate W. Examples of simulations of partially coherent radiation sources that may be used in embodiments of the invention may, for example, include Hyperlith simulations, Prolith simulations, and/or Solid-C simulations. In some embodiments, the simulation can be performed using different configurations of the simulated patterned device MA. For example, the tunable may simulate one or more properties of the patterned device MA and may detect the resulting modulation in the output of the simulation (eg, the simulated radiance intensity profile in the image plane). The amplitude of the detected modulation in the output of the simulation may allow the transfer function of the modulation to be determined. A modulation transfer function that varies according to frequency can be derived. As explained above, the optical transfer function of the optical system (e.g., the modulation transfer function) is equivalent to the power spectral density at which the autocorrelation function can be derived. Autocorrelation function can be used to determine the ratio R_S . In some embodiments, one or more attributes of the simulated patterned device MA can be modulated using an amplitude modulation of approximately 5% or less of the average of the attributes. In some embodiments, the width of the simulated patterned device MA can be modulated as described above. In some embodiments, the ratio R can be determined experimentally._S . For example, a plurality of pulses of the radiation source SO can be used in a single exposure cycle to perform a plurality of exposures. As explained above, the number of pulses to which a spot on a substrate is exposed during a given exposure period affects the number of independent spot patterns that are exposed to that point.N (Assume that the duration of the pulse remains the same). For example, increasing the number of pulses during the exposure period will increase the number of spot patterns that are exposed to the dots on the substrate.N . Figure 12 is a schematic representation of the intensity profile of radiation in an illumination pupil of a lithography system in accordance with an alternate embodiment of the present invention. The lighter regions in Figure 12 indicate the higher intensity of the radiation and the darker regions indicate the lower intensity of the radiation. The radiation is in dipole mode, i.e., has no radiation at the center of the illumination pupil in the y-direction, but has a radiation pole (at the y-direction edge of the illumination pupil) separately in the y-direction. The illumination pupil schematically depicted in Figure 12 has a periodic intensity profile in the x-direction. The intensity profile can be a sinusoidal function of position in the x direction. For each pole of the dipole, the intensity that varies according to the position in the y direction can follow a Gaussian distribution. The intensity distribution of the dipole pole can be configured to provide an isocentric behavior in the manner discussed above in connection with FIG. An advantage of using a dipole illumination mode instead of the centered illumination mode of the type depicted in Figure 5 is that the dipole illumination mode will provide a higher contrast of the image formed on the substrate (W). The dipole illumination mode of the type depicted in Figure 12 can be used, for example, in conjunction with a patterned device having a grating extending in the y-direction. Figure 13 schematically depicts an example of a repeating unit of this grating. The grating can have a distance of approximately 80 nanometers. Each cell of the grating can, for example, have an opaque portion having a width of approximately 40 nm and a transmissive portion having a width of approximately 40 nm. This grating can be used in conjunction with a projection system having a radiation wavelength λ of approximately 193 nm and a numerical aperture NA of approximately 1.35. The patterned device can comprise a conventional (binary) mask (as depicted), an alternating phase shift mask, or an attenuated phase shift mask (eg, having an attenuation of about 6%). In general, the patterned device of any of the embodiments of the present invention may comprise a conventional (binary) mask, an alternating phase shift mask or an attenuated phase shift mask (eg, 6% attenuated phase shifting) cover). In general, the contribution of the spot to the central maximum 13 in the autocorrelation function is the number of independent spot patterns.N Approximate inversely proportional. That is, the contribution of the spot to the center maximum is 1/N Proportionate. The contribution of the non-spot effect to the center maximum is not substantially affected by the number of independent spot patterns.N Change the impact. Therefore, the height of the center maximum 13 is 1/N The gradient that changes and changes is independent of the contribution of the non-spot effect to the maximum height of the center. Instead, the non-spot effect will be independent of 1/N The offset is introduced to the height of the center maximum 13 . A plurality of pulses can be used to perform a plurality of exposures in a given exposure period. As explained above, changing the number of pulses in the exposure period will change the number of independent spot patterns that are exposed to each point on the substrate.N . For each of the plurality of pulses in the exposure period, an autocorrelation function can be derived and the height of the central maximum 13 in the autocorrelation function can be determined. In the case of using this method, the number of independent spot patterns can beN The height change of the center maximum 13 was observed at different values. The height of the center maximum 13 is 1/N The gradient that changes and changes can be determined from this measurement along with the height offset of the center maximum 13 caused by the non-spot effect. This situation allows the contribution of the spot to the height of the center maximum to be separated from the contribution of the non-spot effect to the center maximum. Therefore, the maximum height H of the spot center is determined for each exposure._CS (and therefore the variance due to the spot). This method also allows the ratio R to be determined by also determining the height of the local maximum in the autocorrelation function caused by each exposure._s . The method in which the line width and/or dose variance is caused by the spot has been described above. Additionally or alternatively, the above measurements and methods can be used to determine the number of independent spot patterns that are exposed to a given point on the substrate during the exposure period.N . As explained above, the ratio R_s The decision allows the standard deviation σ caused by the spot to be derived. Number of independent spot patterns exposed to a given point on the substrateN It can be derived from the standard deviation σ by recombining equation (1) to obtain equation (4) below.(4) As described above, one or more exposures may be performed from a single illumination mode to obtain a parameter indicative of the contribution of the spot. The parameters determined using a single illumination mode may be independent of the illumination mode used. For example, a single illumination mode can be used to determine the dose change caused by the spot. The dose change can be independent of the illumination mode used to determine the dose change. Additionally or alternatively, the number of independent spot patterns to which a given point on the substrate is exposed may be determinedN . In some embodiments, it may be used only in the illumination pupil to have a singular numberK A single illumination mode of the cycle to determine the contribution of the spot. This metric can then be applied to all lighting modes. In general, any number in the illumination pupilK The cycles can be selected to perform a measurement procedure to determine the contribution of the spot. As can be seen from equation (2), increase the number of periods in the illumination pupilK The period P that will cause the spot in the image plane to have an effect_s increase. In order to determine the contribution of the spot, it may be necessary to measure a given number of spot periods throughout the image plane._s Line width W_L . Increase the spot period P_s Will result in a given number of spot periods P_s The length of the line feature is increased. Therefore, increase the spot period P_s A line width W that can be measured to determine the contribution of the spot_L The length of the series is increased. As described above, in some embodiments, the line width series can be determined by obtaining an image of the exposed line features using a scanning electron microscope. Scanning electron microscopes can have a limited field of view. If line width W_L If the length of the series is larger than the field of view of the scanning electron microscope, multiple images can be acquired along the length of the line feature and the images can be stitched together to determine the complete line width W._L series. Stitching the images together can introduce errors into the line width W_L In the determination of the series, and therefore, the determination line width W can be reduced_L The accuracy of the series. In some embodiments, it may be necessary to use a sufficiently small numberK Cycles for a given number of spot periods on the substrate W_s Fit to the illumination mode in a single field of view of a scanning electron microscope. This can be avoided in order to determine the complete line width W_L The series requires the stitching of several scanning electron microscope images together. Advantageously, determining the contribution of the spot to changes in the lithography procedure (e.g., dose change or line width variation) as described above may allow for optimization of the lithography procedure while accounting for the contribution of the spot. For example, using the knowledge of spot contribution, other aspects of the lithography procedure can be designed to account for the contribution of the spot. In some embodiments, a post-processing step can be used to reduce the line width roughness after exposing the substrate and developing the substrate. In some embodiments, if the contribution of the spot is found to be too high (eg, the contribution of the spot is determined to exceed the threshold), then action can be taken to reduce the contribution of the spot. For example, one or more attributes of the radiation source SO can be varied to increase the number of individual spot patterns that occur during the exposure period.N . Can increase the number of independent spot patternsN One way would be to increase the number of laser pulses that occur during a single exposure cycle. However, increasing the number of laser pulses that occur during a single exposure cycle can reduce the yield of the lithographic apparatus (the number of substrates exposed per unit time). Additionally and/or alternatively, the pulse duration of the pulses of the radiation beam emitted from the radiation source SO can be increased. For example, one or more pulse stretchers configured to increase the duration of the radiation pulse can be added to the optical path of the radiation beam (eg, added between the radiation source SO and the illumination system IL). Additionally or alternatively, the number of independent spot patterns seen during the exposure period can be increased by increasing the bandwidth of the radiation emitted from the radiation source SON . In embodiments where the radiation source SO comprises a laser, increasing the bandwidth of the radiation emitted from the radiation source SO will increase the number of independent laser modes in effect and thus increase the number of independent spot patterns. Apparatus and methods that allow for determining the contribution of a spot to changes in lithographic features have been described above. Advantageously, this determination can be used to monitor changes in spot contribution resulting from attribute changes of the lithography program. For example, one or more properties of the radiation beam emitted from the radiation source SO can be altered and the resulting change in spot contribution can be measured. For example, the bandwidth of the radiation beam emitted from the radiation source SO and the corresponding change in spot contribution can be measured. It has been experimentally shown that reducing the bandwidth of the radiation beam emitted from the self-radiating source SO causes an increase in the contribution of the spot width roughness. Advantageously, determining the change in spot caused by the change in bandwidth would allow for an assessment of the benefit of changing the bandwidth and allowing selection of the appropriate bandwidth to produce the desired result. Figure 14 is a photograph showing a line of a grating that has been imaged onto a substrate using a lithography apparatus. The radiation has a wavelength of 193 nm and is x-polarized. The reticle is an alternating phase shift mask with a grating having a pitch of approximately 160 nm. The numerical aperture of the lithography apparatus is 1.35. The illumination mode has an x-direction modulation of 700 nm and has 7 cycles (K =7) The single axis upper pole. A scanning electron microscope was used to produce the photo. As can be seen, the grating extends in the y-direction (i.e., it is periodic in the y-direction), with individual lines of the grating extending in the x-direction. As explained above, the width W of each line that varies according to the position in the x direction can be measured._L . The resulting width data for each line can then be correlated with itself (i.e., the width of each line is related to itself along the length of the x-direction). This situation provides an autocorrelation function that can be used to determine how much line width variation (equivalent to critical dimension variation) is caused by the spot. As explained above, a generally applicable measurement (ie, irrelevant to the illumination mode) using an autocorrelation function to obtain the contribution of the spot may include measuring the intensity profile of the illumination pupil or generating a simulation of the intensity profile. The following is a description of alternative methods that are simpler and easier to implement than the above methods. Instead of performing auto-correlation along one dimension of each line in the x direction, a two-dimensional correlation is performed. Referring to Figure 14, the width W of each line along the x direction is performed._L Autocorrelation. Execute the width of each line relative to the next adjacent line W_L The x-direction correlation. The width of each line relative to a line that is not adjacent but below the adjacent line (ie, the line separated by an intermediate line) is performed._L The x-direction correlation. Execute the width of each line relative to the line separated by two intermediate lines W_L The x-direction correlation. Also performs line width W for larger separation distance between lines_L Another x-direction correlation. As explained further above, the width of the imaged line varies depending on the position in the x direction, wherein the portion of the width change is caused by the spot. The change in width is caused by the change in intensity of the radiation that forms the line, and this change in intensity is caused by the spot. Therefore, the standard deviation σ of the line width (which may be referred to as the critical dimension standard deviation) depends in part on the spot. It has been found that the position of the line in the y direction also includes some variation including the contribution caused by the spot. The position of the line in the y direction is affected by the gradient of the intensity change at the edge of the line (i.e., the rate at which the intensity changes from high intensity to low intensity). The gradient of intensity change is affected by the spot. Therefore, the standard deviation σ of the line position dY depends in part on the spot. Figure 15 is a graph generated using simulation. The simulation uses the same parameters as the experimental setup used to generate the image in Figure 14. That is, an alternating phase shift mask having x-polarized radiation having a wavelength of 193 nm, a grating having a pitch of 160 nm, and a numerical aperture of a lithography apparatus of 1.35. Uses an x-direction modulation of 700 nm with 7 cycles (K =7) The single axis upper pole. The simulation is performed using a simulated lithography projection system using tens of thousands of Monte Carlo simulations of a radiated E-field having an amplitude of 1 and a random phase (distributed between -180 degrees and +180 degrees). As can be seen from Fig. 15, the standard deviation σ of the critical dimension CD of the line varies linearly according to 1/sqrt(N). As further mentioned above, the measure of spot contribution independent of the illumination mode used comprises the number N of individual spot patterns exposed to a given point on the substrate during a single exposure period. When the source SO is a laser, the number N of independent spot patterns is equal to the number of independent laser modes in the excitation of the laser during the exposure period. Therefore, the relationship between the critical dimension of the line and the spot is confirmed based on the linear change in the standard deviation of the critical dimension of the line of 1/sqrt(N). As can also be seen from Fig. 15, the standard deviation σ of the position y in the y direction of the line also varies linearly according to 1/sqrt(N). Therefore, the position y in the y direction of the line has the same dependence on the spot as the critical dimension of the line. Although the effect of the spot on the y-direction position dY is less strong than the effect of the spot on the critical dimension CD (this is because it is linear with respect to the 1/sqrt(N) system), it can still be used to aid spot determination. The effect on the line position change dY is smaller than the effect on the CD change, because the gradient of the intensity change is relatively small compared to the intensity change. Figure 16 depicts a two-dimensional correlation function generated using simulation. The correlation function (in square nanometers) is expressed in terms of the positional offset (in microns) along the line. As can be seen, the correlation function includes a center maximum and a first local maximum and a second local maximum separated from the central maximum. As explained further above, the first local maximum and the second local maximum are caused by periodic modulation of the spot combined illumination mode. In the y direction corresponding to the distance from the y direction of the line, these maximum values are attenuated as the distance in the y direction increases. The zero position of dY corresponds to the correlation of each line to itself, and (as expected) provides the highest maximum. On either side of the zero position, the correlation function is the correlation of the line width of each line relative to adjacent lines. Either side of this correlation function is a combination of the line width of each line relative to the second adjacent line (i.e., the line separated by the intermediate line), and the like. As the distance between the correlation lines (according to the number of lines) increases, the maximum value of the two-dimensional correlation function is reduced. Figure 17 depicts experimental results obtained using the images depicted in Figure 14. The results are shown for each line's relevance to itself, the relevance of each line to the adjacent line, the correlation of each line to the second adjacent line, and the like. As can be seen, the top of the center maximum of the autocorrelation function is not visible when each line is correlated with itself. However, the top of the center maximum of the autocorrelation function is visible when correlating adjacent lines. Similarly, the top of the center maximum is visible when the second adjacent line is correlated. As the separation distance between the correlation lines increases, the height of the center maximum is reduced. In other words, the larger the distance between the lines associated with each other, the smaller the maximum value of the autocorrelation function becomes. The data depicted in Figure 17 can be used to determine the effect of the spot. First, the background level is determined by looking at data obtained by using lines that are widely separated from each other (eg, separated by 7 intermediate lines or more), and this background bit is subtracted from the data obtained for other lines. quasi. Next, determine the height H of the local maximum for different line distances._LS Height H with the center maximum_CS Ratio between R_S . The average of this ratio is then determined. Then combine the maximum height H of the spot area for the line associated with itself_LS To use the average ratio R_S To estimate the height H of the center maximum caused by the spot used for the line associated with itself_CS . This H_CS The CD variance of the line of the image caused by the spot is determined (in other words, the contribution to the spot of the center maximum). The CD variance due to the spot (as measured in square nanometers) can be converted to a dose change and thereby used to determine the number N of independent spot patterns of the radiation source. This can be accomplished by using experimental data that links changes in feature size (eg, line width) to the radiation dose delivered to the substrate. A so-called focus exposure matrix can be used to generate experimental data in which the grating is exposed to the substrate using different radiation doses and using different positions relative to the focal plane, and the width of the line through the imaging grating is measured. The relationship between the line width and the dose is applied to the CD variance caused by the spot to convert it into a dose variance caused by the spot (which may be equivalently referred to as the intensity variance). This dose variance can then be converted to a measure of the number N of independent spot patterns of the radiation source (or the number of independent laser modes if the source is laser) using equation (1). While embodiments have been described using specific parameters such as the particular reticle grating size, it should be understood that other embodiments may be utilized. In general, a pattern comprising a grating that will form an image of the line on the substrate can be used. This pattern can be used in conjunction with a modulated illumination mode. Variations in the width of a line associated with itself and associated with other lines can be analyzed to determine the spot. In an embodiment, the change in position of line dY can be used to determine the spot. This can be done by associating the positional changes of the line dY for each line, each adjacent line, a line separated from each other by a middle line, and the like. This two-dimensional correlation result can then be used in conjunction with the simulation of the effect of the spot on the change in line position to determine the spot (in a manner similar to that described above for other embodiments). Figure 18 schematically depicts an illumination mode that may be used by an alternate embodiment of the present invention. The illumination mode is a quadrupole mode having poles at the x-direction edge and the y-direction edge of the illumination pupil. Unlike the illumination modes of the previously depicted embodiments, each pole of the illumination mode of Figure 18 does not include modulation. However, the illumination mode as a whole actually includes some modulation due to the spatial separation between the opposite poles of the mode. Figure 19 schematically depicts a repeating unit of a pattern provided on a patterned device that can be used in conjunction with the illumination mode of Figure 18 to enable measurement of the spot. The pattern contains a two-dimensional grid of squares. For example, a square can be opaque (eg, formed of chrome) with a transparent region provided between the squares. In one example, as depicted, each square can be 40 microns by 40 microns in size, and each square can be separated from adjacent squares by a gap of 40 microns in the x and y directions. Thus, repeating units (as depicted) having dimensions of 80 microns by 80 microns are provided. The illumination mode and the pattern can be used, for example, for a radiation source having a wavelength of 193 nm and a projection system having a numerical aperture of 1.35. In other embodiments, the pattern may comprise a two-dimensional grid having other dimensions. A binary (conventional) reticle, phase shift reticle, or attenuated phase shift reticle can be used to form the pattern. The pattern on the patterned device produces a grid (or two-dimensional array) of features on the substrate. These features may be referred to as holes. Scanning electron microscopes can be used to photograph the holes and the properties of the holes can then be analyzed. The quadrupole illumination mode produces a diffraction pattern in the form of a two-dimensional array of features. The orientation and spacing of the features of the two-dimensional array is determined by the quadrupole illumination mode. The orientation can be selected to correspond to the x and y directions by separating the poles in the x and y directions (as depicted). The distance between features is determined by Braggs' law and depends on the wavelength of the radiation and the distance between the opposite poles. In this embodiment, the wavelength is 193 nm and the separation distance between the poles is 193/80 = 2.41. Therefore, the feature is optimally imaged with a relative polar position of 193/(80x2x1.35) = 0.89 (center point from the pupil) and a relative distance of 1.78 from each other. The image formed on the substrate is a combination of a pattern produced by the reticle pattern and a diffraction pattern produced by a quadrupole illumination mode. The change in the size of the imaged aperture corresponding to the critical dimension change can be measured. The change in relative position in the x-direction (dX) and the y-direction (dY) of the imaging aperture can also be measured. The results of these measurements can be used to determine the effect of the spot. This is because the spot appears as a correlation between the properties of adjacent holes. Figure 20 shows the results of the simulation in which a four-pole pattern as depicted in Figure 18 is used to illuminate a patterned device having a square grid as depicted in Figure 19. The wavelength of the radiation was 193 nm, polarized by TE, and the numerical aperture of the lithography apparatus was 1.35. The simulation is performed using tens of thousands of Monte Carlo simulations of a radiated E-field with an amplitude of 1 and a random phase (distributed between -180 and +180 degrees). As can be seen from Fig. 20, the standard deviation σ of the critical dimension CD of the hole varies linearly according to 1/sqrt(N). The relationship between the critical dimension of the hole and the spot is confirmed by the linear change of 1/sqrt(N). As can also be seen from Fig. 20, the standard deviation σ of the position xX of the hole in the x direction varies linearly according to 1/sqrt(N). Therefore, the x-direction position dX of the hole has the same dependence on the spot as the critical dimension of the line, that is, it is linear according to the 1/sqrt(N) system. The magnitude of the effect of the spot on the x-direction position dX is very similar to the magnitude of the effect on the critical dimension CD. As can be seen from a comparison with Fig. 15, the change in the standard deviation of the hole position according to 1/sqrt(N) is significantly larger than the change in the position seen by the grating line. This is because the gradient of the intensity change for the features of the grid is steeper than the gradient for the intensity change of the grating lines. As can also be seen from Fig. 20, the standard deviation σ of the position y in the y direction of the hole also varies linearly according to 1/sqrt(N). The magnitude of the effect of the spot on the y-direction position dY is very similar to the magnitude of the effect on the critical dimension CD and the magnitude of the effect on the x-direction position dX. The total variance of the critical dimensions of the holes is affected by the spot and is affected by various other factors. However, the correlation between the critical dimensions of adjacent holes is only affected by the spot and is not affected by other properties of the radiation. Similarly, the change in position in the x-direction between adjacent holes and the change in position in the y-direction are only affected by the spot and are not affected by other properties of the radiation. Using the results of the simulation, the two-dimensional autocorrelation of the critical dimensions of the pores can be determined. In other words, the autocorrelation of the hole size is determined for the grid of holes to obtain an autocorrelation function. The correlation of the hole size for the grid of holes with respect to the adjacent holes in the x direction is also determined. The correlation of the hole size for the grid of holes with respect to the holes separated by an intermediate hole in the x direction is determined. The correlation of the hole size for the grid of holes with respect to the holes separated by the two intermediate holes in the x direction is determined, and so on. The corresponding correlation in the y direction is determined. Correlation is also performed for the combination of the x-direction distance and the y-direction separation between the holes. Figure 21 depicts the results of the simulations mentioned above. The two-dimensional correlation of the aperture size in the simulated image is produced by determining the size of all the holes in the x-direction and the y-direction according to the x-direction and the y-direction separation and then correlating the holes according to the distance from each other. In Figure 21, the center maximum is the correlation of the size of each well to itself (autocorrelation). The magnitude of this maximum value indicates the total variance of the critical dimensions caused by the spot (other reasons for seeing critical dimension changes when actually using lithographic devices that are not present in the simulation to form an image). On either side of the center maximum, the correlation of the critical dimensions for adjacent holes is also determined solely by the spot. The data generated by the simulation is used to determine the relative magnitude of the critical dimension variance at the center maximum and the critical dimension variance at the center maximum. The reticle device is used to project the reticle pattern of Figure 19 onto the substrate using radiation having the illumination pattern depicted in Figure 18. The radiation has the properties described above for the simulation: wavelength 193 nm, and the like. The two-dimensional correlation of the pore sizes in the resulting image is produced by determining the size of all of the holes in the x-direction and the y-direction based on the x-direction and the y-direction position and then correlating the holes in relation to the position of the holes relative to each other. The central maximum obtained using the two-dimensional correlation indicates the total variance of the critical dimensions, including the variance caused by the flare and the variance due to other causes. On either side of the center maximum, the critical dimension variance for adjacent holes is determined solely by the spot (or almost entirely by the spot). This is because the distance between the holes is sufficiently large that other effects with short correlation lengths do not extend to adjacent holes (or such effects are extremely small at adjacent holes). In the case of using the simulation, it has been determined that the relative size (ratio) of the critical dimension variance at the center maximum value and the critical dimension variance of the center maximum value are any size. The magnitude of either side of the critical dimension variance of the center maximum in the image exposed by the lithography apparatus has been measured. In the case where the ratio is known and the size of either side of the critical dimension variance for the maximum value of the exposed image is known, it is allowed to determine the magnitude of the center maximum caused only by the spot. In other words, the critical size variance of the holes caused only by the spot is determined. The critical dimension variance of the hole caused by the spot is determined in units of square nanometers. This critical dimension variance can be converted to a dose change caused by the spot and converted to the number N of independent spot patterns of the radiation source, as explained above in connection with the previous embodiments. 22 and 23 depict the results of the same simulation, but this display indicates the change in the y-direction position dY of the hole according to the distance between the holes (Fig. 22) and the change in the x-direction position dX according to the distance of the hole ( Figure 23) Information. The data obtained from the simulation can be used with an image formed using a lithography apparatus to determine the spot in the same manner as described above in connection with the critical dimension change. Although embodiments have been described that use specific parameters such as pattern feature size, it should be understood that other embodiments may be utilized. In general, a pattern comprising a two-dimensional array of pattern features that will form a two-dimensional array of image features on the substrate can be used. The pattern can be used in conjunction with an illumination pattern that will produce a two-dimensional diffraction pattern comprising an array of features. The features of the two-dimensional diffraction pattern can have the same spacing and orientation as the imaged pattern features. Critical dimension changes, such as features associated with themselves and associated with other features, can be analyzed to determine the spot. Location changes such as features associated with itself and associated with other features can be analyzed to determine the spot. Specific embodiments of methods and apparatus for measuring the contribution of a spot have been described above with reference to the figures. However, other embodiments of the invention may differ from the specific details described above. Although the embodiments of the present invention have been described above with reference to lithography apparatus LA, the present invention can be used to determine that an illumination system configured to illuminate a patterned device is configured and configured to project a patterned radiation beam onto an image plane The contribution of the spot in any optical system of the projection system. 24 is a flow chart outlining the steps of a general method for measuring the spot effect in an optical system in accordance with an embodiment. At step S1, the illumination system is configured to form a periodic illumination mode. The periodic illumination mode includes a spatial intensity profile that is periodic in at least one direction in the pupil plane of the illumination system. For example, the intensity of the radiation in the pupil plane may be substantially sinusoidal depending on the position in the pupil plane in at least one direction (eg, the x direction) (eg, a cosine function such as 1+cos(x)) . The spatial intensity profile in the pupil plane may not be periodic in some directions. For example, the spatial intensity profile may be periodic in the x-direction but may not be periodic in the y-direction. The spatial intensity profile can, for example, follow a Gaussian distribution in the y-direction. The periodic spatial intensity profile can include in the pupil planeK Cycles.K Can be an integer.K Can be odd.K Can be greater than 2.K It can be, for example, 5 or more. In some embodiments,K It can be about 17 or less. A patterned device in an illumination mode illumination optical system. The patterned device imparts a pattern to the radiation, thereby forming a patterned beam of radiation. The spatial intensity profile of the radiation in the pupil plane determines the angular intensity profile of the illumination of the illumination patterned device. Thus, the periodic spatial intensity profile in the pupil plane will illuminate the patterned device with a periodic angular intensity profile. At step S2, the dose of radiation received in the image plane of the optical system that varies according to the position in the image plane is measured. The patterned radiation beam is projected onto the image plane by a projection system. The patterned radiation beam can, for example, include one or more line features (ie, lines of radiation). The received radiation dose can be measured directly or indirectly. For example, the substrate can be positioned in the image plane and the substrate can be exposed to a patterned beam of radiation. One or more features of the patterned radiation beam can be transferred to the substrate by exposure of the substrate to the one or more features. For example, a resist can be provided on the substrate. Exposure of the resist to the characteristic of the patterned radiation beam can cause a change in the state of the exposed portion of the resist. The resist can be developed, for example, using an etch process to form one or more features of the patterned radiation beam in the resist. The developed resist may form a reticle for etching features into the substrate to transfer features into the substrate. In an embodiment where the features of the patterned radiation beam are transferred to a substrate. The dose of radiation received in the image plane can be indirectly measured by measuring the size of one or more features in the substrate. For example, the width of a feature in a substrate can be approximately proportional to the dose of radiation received at that location in the image plane. Thus, measuring the width of the feature that varies depending on the position on the substrate allows for determining the dose of radiation received in the image plane that varies according to the position in the image plane. The size of one or more features in the substrate can be measured, for example, using a scanning electron microscope. A scanning electron microscope can be used to form an image that is patterned into features in the substrate. The size of the feature can be measured by performing image analysis on the image that is patterned into features in the substrate. For example, one or more edges of the feature can be detected in the image to determine the location of the edge of the feature (eg, the edge of the line feature). The position of the edge of the feature can be used to determine the size of the feature. For example, the width of the feature can be determined at different locations of the feature. In some embodiments, the width of the line feature can be determined at different locations along the length of the line. Thus, the measured width of the feature that varies depending on the position on the substrate may allow for determining the dose of radiation received in the image plane that varies according to the position in the image plane. In some embodiments, a plurality of features can be exposed and the size of the plurality of features can be measured. For example, in some embodiments, more than about 100 line features can be exposed and the line width of each feature can be measured, thereby providing more than about 100 line width series for a given illumination mode. In some embodiments, more than about 1000 line features can be exposed for a given illumination mode to provide more than about 1000 line width series. A plurality of line width series for a given illumination mode can be used to calculate an average power spectral density at a plurality of spatial frequencies for the given illumination mode. A device configured to measure a radiation dose received in the image plane that varies according to the position on the image plane can be considered a measurement system. The metrology system can include a substrate stage configured to hold the substrate in an image plane of the projection system to receive the patterned radiation beam. The substrate may be provided with a resist. The metrology system can further include means configured to develop the resist and transfer the pattern to the substrate, as described above. A device configured to apply a resist to a substrate and develop the resist may be referred to as a coating development system. The metrology system can further include a sensor configured to detect a size of a feature at a different location on the substrate in the substrate. For example, the metrology system can include a sensor (eg, a scanning electron microscope) configured to form an image of features in the substrate. The metrology system can further include means (eg, a controller) configured to determine the size of features in the substrate. For example, the controller can process the image to detect the position of one or more edges of the feature (eg, the edge of the line feature) and can determine the size of the feature from the detected position of the edge. The controller can be further configured to determine the dose of radiation received in the image plane from the determined size of the feature. The feature on the substrate is exposed and the size of the exposed features is measured to determine that the dose of radiation is merely one example of a method for determining the received radiation dose in the image plane that varies according to the position in the image plane. In other embodiments, other methods for measuring the received radiation dose can be used. In some embodiments, the radiation received in the image plane can be directly measured, for example, using a sensor positioned substantially in the image plane. The sensor measures the spatial intensity profile of the radiation at different locations in the image plane in the image plane. Due to the small size of the features of the spatial intensity profile in the image plane, in some embodiments, the magnified image of the spatial intensity profile in the image plane can be formed in an additional image plane. The sensor can be positioned substantially in the additional image plane and can be configured to measure an enlarged image of the spatial intensity profile in the image plane. For example, the sensor can include a camera. A device configured to measure the spatial intensity profile of radiation in an image plane can be considered an example of a measurement system. For example, the metrology system can include a sensor configured to measure a spatial intensity profile of radiation at different locations in the image plane in the image plane. In some embodiments, the metrology system can include one or more optical components configured to form an enlarged image of the image plane in an additional image plane. The sensor can be positioned substantially in the additional image plane. The metrology system can further include a controller configured to determine the received radiation dose at different locations in the image plane. At step S3, the dose change in the image plane is selected to be one or more spatial frequencies at which the spot is caused. The one or more spatial frequencies at which the spot causes the dose change depends on the period of the periodic intensity profile in the pupil plane of the illumination system. The period of the periodic intensity profile in the pupil plane of the illumination system (or equivalently, the period in the pupil planeK The number) can be used to select one or more frequencies. For example, equation (2) above can be used to select one or more frequencies. At step S4, a measure of the dose change at one or more spatial frequencies is determined. A measure of dose change is indicative of a spot in the image plane. For example, the metric can include an autocorrelation function of the first series and the second series. The first series can be a measured size of the features of the patterned radiation beam at different locations in the image plane. The second series can be identical to the first series, and the autocorrelation function between the first series and the second series can be calculated when the second series is offset relative to the first series. An autocorrelation function can be calculated at a position offset between the second series and the first series, the position offset being equal to the reciprocal of one or more spatial frequencies selected in step S3. That is, the amount of positional offset may be equal to the spatial period during which the change in the measured dimension is caused by the spot. The magnitude of the autocorrelation function at this offset is an indication of the spot in the image plane. The spatial frequency selected in step S3 may correspond to the position offset in the autocorrelation function in which the local maximum is seen. Therefore, the magnitude of the autocorrelation function at the position offset corresponding to the frequency selected in step S3 may be the height of the autocorrelation function at the local maximum of the autocorrelation function. The spatial frequency selected in step S3 can be selected, for example, by finding the local maximum in the autocorrelation function. The position offset at which the local maximum is seen may correspond to the selected spatial frequency. That is, the spatial frequency of 1 can be obtained by seeing the position offset at which the local maximum is located. Reference herein to a local maximum refers to a region where a function (eg, an autocorrelation function) reaches a local maximum that is not the maximum of the entire function. Therefore, the reference to the local maximum is not intended to include the region where the function is at the global maximum (eg, the central maximum). Reference herein to the central maximum in the autocorrelation function is intended to refer to the region of the autocorrelation function in which the autocorrelation function is at the global maximum. A measure of dose change can be used to derive a measure of the spot in the image plane that is independent of the illumination mode used. For example, a measure of dose change can be used to derive the variance (or equivalently, standard deviation σ) of the measured dose caused by the spot in the image plane. In an embodiment in which the autocorrelation function is determined using the dimensions measured in step S2, the variance of the measured dose caused by the spot in the image plane corresponds to the self of the spot pair at the global maximum of the autocorrelation function. The contribution of the height of the correlation function. In some embodiments, the height of the autocorrelation function at the local maximum of the autocorrelation function can be used to derive the contribution of the spot to the height of the autocorrelation function at the global maximum of the autocorrelation function. For example, a ratio between the height of the local maximum in the autocorrelation function representing the contribution of the spot to the change in the measured dose and the height of the global maximum can be determined. The determined ratio can be used to scale the height of the measured autocorrelation function at the local maximum to find the contribution of the spot to the height of the global maximum in the autocorrelation function. One or more of the steps shown in Figure 24 and described above may be performed by a controller. For example, the controller CN shown in FIG. 1 can perform one or more of the steps shown in FIG. 24 and described above. The controller CN as described herein may comprise a computer in some embodiments. The computer can, for example, include a central processing unit (CPU) configured to read and execute instructions stored in volatile memory in the form of random access memory. Volatile memory stores instructions for execution by the CPU and materials used by them. The embodiment has been described above with reference to a lithography apparatus LA comprising: an illumination system IL configured to illuminate the patterned device MA to form a patterned radiation beam; and a projection system PL configured To project the patterned radiation beam onto the image plane. However, the devices and methods described herein are suitable for determining the contribution of a spot in other optical systems that may not be lithographic devices. As described above, the use of a patterned device to form a patterned radiation beam to form a pattern feature in the image plane and then to measure the size of the pattern features in the image plane is only used to determine the received radiation dose in the image plane An example of a method. In other embodiments, the patterned device may not be used, and the received radiation dose in the image plane may be measured by other suitable means depending on the location in the image plane. Although the embodiments described above refer to measuring the received radiation dose in the image plane (usually the plane in which the substrate is located), in other embodiments, in any plane optically conjugated to the image plane The received radiation dose is measured. For example, the received radiation dose can alternatively be measured in the object plane of the optical system, wherein the object plane is a conjugate plane of the image plane. An example of an object plane in a lithography system can be the plane in which the patterned device MA is typically located. Any plane that is optically conjugate to an image plane (eg, an object plane) may be referred to herein as a field plane. Thus, examples of field planes include image planes (eg, the plane on which substrate W is typically located) and object planes (eg, where patterned device MA is typically located). In general, the contribution of the spot can be determined using the methods described herein by measuring the dose of radiation received in any field plane of the optical system that varies according to the position in the field plane. The field plane can be, for example, an image plane or an object plane of the optical system. Thus, any reference herein to the radiation dose in the image plane of the metrology optical system can be equivalently substituted for the radiation dose in the field plane. In general, the inventive concepts disclosed herein can be used to determine the contribution of a spot in any optical system that includes an illumination system that is operable to form a periodic illumination pattern in the pupil plane of the optical system. Advantageously, the periodic illumination pattern in the pupil plane is used to limit the effects of the spot to a limited number of spatial frequencies in the field plane of the optical system. Advantageously, this situation allows the contribution of the spot to the dose change in the field plane to be separated from the contribution of other effects. The pupil plane of the optical system is a plane having a Fourier relationship with the field plane. That is, each spatial point in the pupil plane corresponds to an angle in the corresponding field plane, and vice versa. Aspects of the invention may be practiced in any convenient form. For example, the invention can be implemented by a suitable computer program executable on a suitable carrier medium, which can be a tangible carrier medium (eg, a magnetic disk) or an intangible carrier medium (eg, a communication signal). The present invention can also be implemented using suitable means, which can be embodied in the form of a programmable computer that executes a computer program configured to carry out the invention. Although the specific embodiments of the invention have been described above, it is understood that the invention may be practiced otherwise than as described. This description is not intended to limit the invention.

11a‧‧‧ First immersion feature 11b‧‧‧Second basal feature 13‧‧‧Center maximum 15a‧‧‧First local maximum 15b‧‧‧Second local maximum 101‧ ‧First curve 103‧‧‧Second curve 105‧‧‧ Third curve 107‧‧‧Fourth curve 109‧‧‧Fifth curve AM‧‧‧Adjusting components BD‧‧‧ Beam delivery system C‧‧‧ Target Part of the CN‧‧‧ controller CO‧‧‧ concentrator H _L ‧‧‧High IF‧‧‧ position sensor IL‧‧‧Lighting system IN‧‧‧ illuminator M1‧‧‧ patterned device alignment Marking M2‧‧‧ patterned device alignment mark MA‧‧‧patterned device MT‧‧‧Support structure/object table P1‧‧‧Substrate alignment mark P2‧‧‧Substrate alignment mark PB‧‧‧radiation beam PL ‧‧‧ projection system PM‧‧‧ first positioning means _{P p} ‧‧‧ period P _s ‧‧‧ PW‧‧‧ second positioning means from the radiation source S1‧‧‧ SO‧‧‧ step S3 step S2‧‧‧ ‧‧‧ step S4‧‧‧ W‧‧‧ step width of the substrate W _L ‧‧‧ WT‧‧‧ substrate table / object table

Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which FIG. Schematic description; - Figure 2 is a representation of lithographic features that may be formed using the lithography apparatus of Figure 1; - Figure 3 is a representation of the power spectral density associated with the dimensions of the lithographic features shown in Figure 2; - Figure 4 is a representation of the autocorrelation function associated with the dimensions of the lithographic features shown in Figure 2; - Figure 5 is the space of the radiation in the pupil plane of the illumination system forming part of the lithography apparatus of Figure 1. a representation of the intensity profile; - Figure 6 is a representation of the autocorrelation function associated with the size of the lithography feature; - Figure 7 is a representation of the autocorrelation function associated with the size of the lithography feature formed using the different illumination modes; - Figure 8 is a representation of the position of the local maximum in the autocorrelation function of Figure 7; - Figure 9 is a representation of the height of the local maximum in the autocorrelation function of Figure 7; - Figure 10 is for the illumination system Radiation space in the pupil plane a representation of the autocorrelation function associated with the intensity profile; - Figure 11 is a representation of the height of the local maximum of the autocorrelation function associated with the different spatial intensity profiles of the radiation in the pupil plane of the illumination system; - Figure 12 is Illumination mode used by an embodiment of the present invention; - Figure 13 is a unit for patterning radiation used by an embodiment of the present invention; - Figure 14 is a line formed using the illumination modes and patterns of Figures 12 and 13 Figure 15 is a graph obtained using simulations depicting the standard deviation of the critical dimension and line position change according to 1/sqrt (the number of independent spot patterns); - Figure 16 is a depiction using Figure 12 and Figure 2 is a two-dimensional correlation image of the critical dimension obtained from the simulation of the illumination mode and pattern; - Figure 17 is a graph depicting the measurement results of the two-dimensional correlation between the lines of the image of Figure 14; - Figure 18 is a graph Illumination mode used by an embodiment of the present invention; - Figure 19 is a unit used to pattern a pattern of radiation by an embodiment of the present invention; - Figure 20 is a graph obtained using simulation, It depicts the critical dimension and the standard deviation of the change in feature position according to 1/sqrt (the number of independent spot patterns); - Figure 21 depicts the critical dimensions obtained from the simulation using the illumination modes and patterns of Figures 18 and 19. 2D related image; - Fig. 22 is a two-dimensional correlation image depicting changes in the y-direction position of the feature obtained from the simulation using the illumination modes and patterns of Figs. 18 and 19; - Figure 23 is a diagram depicting the use of Figure 18 and A two-dimensionally correlated image of the positional change in the x-direction of the feature obtained from the simulation of the illumination mode and pattern of 19; and - Figure 24 is a representation of the steps of the method in accordance with an embodiment of the present invention.

S1‧‧‧ steps

S2‧‧‧ steps

S3‧‧‧ steps

S4‧‧‧ steps

Claims (40)

An optical system comprising: an illumination system configured to form a periodic illumination mode, the periodic illumination mode comprising radiation in a pupil plane of the optical system, the radiation having at least one direction a periodic spatial intensity profile; a metrology system configured to measure a radiation dose received in a field plane of the optical system that varies according to a position in the field plane; and a controller, It is configured to: select a change in the received radiation dose that varies depending on the location in the field plane by one or more spatial frequencies at which the spot is located; and at the selected one or more spatial frequencies A measure of the change in the received radiation dose that varies depending on the location, the measure of the change in the received dose indicating a spot in the field plane. The optical system of claim 2, wherein the illumination system is configured to illuminate a patterned device with a radiation beam, the patterned device configured to impart a pattern to the radiation beam in a cross section of the radiation beam In order to form a patterned radiation beam. The optical system of claim 1 or 2, further comprising a projection system configured to project a radiation beam onto a field plane. The optical system of claim 1 or 2, wherein the controller is further configured to determine a contribution of the spot to the change in the received dose, the contribution of the spot being used at the selected one or more spatial frequencies The measure of the change in the received dose is determined. The optical system of claim 4, wherein the determined contribution of the spot to the change in the received dose comprises a variance of the dose caused by the spot. The optical system of claim 1 or 2, wherein the controller is configured to determine the metric in the change in the received dose at the selected one or more spatial frequencies in the field for a given period of time The number of independent spot patterns received in the plane. The optical system of claim 1 or 2, wherein the measuring system comprises: a substrate stage configured to hold a substrate substantially in the field plane to expose the substrate to the patterned radiation beam; And a sensor configured to detect a size of one of the features patterned into the substrate at different locations on the substrate, patterned according to a location on the substrate The dimension of the feature in the substrate provides a measure of the radiation dose received in the field plane as a function of position in the field plane. The optical system of claim 7, wherein the sensor comprises: a scanning electron microscope configured to acquire an image of the feature patterned onto the substrate; and a controller configured to The image is sized to detect one of the features at different locations on the substrate. The optical system of claim 7, wherein the measurement system further comprises a coating development system configured to apply a resist to a substrate and after exposing to a patterned radiation beam The resist is developed to transfer the pattern to the substrate. The optical system of claim 1 or 2, wherein the controller is configured to determine an autocorrelation function of a first series and a second series, wherein the first series is included at different locations in the field plane The received radiation dose in the field plane is measured, and the second series is identical to the first series and offset from the first series by a position offset. The optical system of claim 10, wherein the controller is configured to evaluate the autocorrelation function at a position offset for one of a reciprocal of the one or more selected spatial frequencies. The optical system of claim 11, wherein the position offset for the reciprocal of the one or more selected spatial frequencies indicates that the autocorrelation function is substantially at a position offset of one local maximum. The optical system of claim 11, wherein the autocorrelation function evaluated at a positional offset for the inverse of the one or more selected spatial frequencies provides a spot pair that varies according to the position in the field plane. A measure of the contribution of one of the received radiation doses. The optical system of claim 13, wherein the controller is further configured to scale the autocorrelation function evaluated at a position offset for the inverse of the one or more selected spatial frequencies and to determine the field The total variance of the received radiation dose caused by the spot in the plane. The optical system of claim 14, wherein the controller is further configured to: determine a local maximum of one of the spot autocorrelation functions corresponding to one of the doses in the field plane caused by only the spot a ratio of one of the global maximum values; and the autocorrelation function evaluated at a positional offset for the reciprocal of the one or more selected spatial frequencies is scaled according to the determined ratio. The optical system of claim 15 further comprising a sensor device configured to measure the spatial intensity profile of the periodic illumination pattern in the pupil plane of the optical system, wherein The controller is configured to determine a ratio of a local maximum from a local autocorrelation function to a global maximum from the measured spatial intensity profile of the periodic illumination mode, wherein the spot corresponds to a correlation function One of the doses in the field plane caused by only the spot changes. The optical system of claim 15, wherein the controller is configured to perform a simulation of one of the radiation propagating through the optical system, and from the simulation determining a change corresponding to one of the doses in the field plane caused by only the spot The ratio of one local maximum to one global maximum in a spot autocorrelation function. The optical system of claim 1 or 2, further comprising a radiation source configured to provide a radiation beam to the illumination system, wherein the radiation source is operable to adjust an attribute of the radiation beam to change The number of independent spot patterns received in the field plane per unit time. The optical system of claim 18, wherein the radiation source is configured to provide a pulsed radiation beam to the illumination system, and wherein the radiation source is operative to adjust a duration of a pulse of radiation emitted from the radiation source, Thereby the number of independent spot patterns received in the field plane per unit time is varied. The optical system of claim 18, wherein for each configuration of the adjustable property of the radiation source, the controller is configured to: select a change in the received radiation dose that varies depending on location in the field plane One or more spatial frequencies at which the spot is caused; and a measure of the change in the received radiation dose as a function of position at the selected one or more spatial frequencies, the received dose This measure of change indicates the spot in the field plane. The optical system of claim 20, wherein the controller is further configured to evaluate the measure of the change in the received dose under a plurality of configurations of the adjustable property of the radiation source, and from the evaluation This contribution of the spot to this change in the received dose under each configuration. The optical system of claim 1 or 2, wherein the controller is configured to select the measured dimension in the field plane using a number of periods of the spatial intensity distribution in the pupil plane of the optical system The change is caused by the spot by the one or more spatial frequencies. An optical system as claimed in claim 22, wherein the controller is configured to select the spatial dimension P _s according to an equation to select the change in the measured dimension in the field plane that is caused by the spot One or more spatial frequencies: Where K is the number of periods of the spatial intensity distribution in the pupil plane of the optical system, λ is the wavelength of the radiation beam and NA is the numerical aperture of the optical system, wherein the measurement is in the field plane Alteration of the size of the light spot caused by the one or more spatial frequencies for which the reciprocal of the spatial period P _s. The optical system of claim 1 or 2, wherein the illumination system comprises a mirror array that is adjustable to adjust the spatial intensity profile in the pupil plane of the optical system. The optical system of claim 1 or 2, wherein the illumination system is configured to form a periodic illumination mode comprising radiation in a pupil plane of the optical system, the radiation having a first A periodic spatial intensity profile in the direction, wherein the periodic spatial intensity profile comprises K cycles. The optical system of claim 25, wherein the illumination system is configured such that the spatial intensity profile substantially follows a Gaussian distribution in a second direction, wherein the second direction is substantially perpendicular to the first direction. The optical system of claim 25, wherein K is an integer. The optical system of claim 27, wherein K is an odd number. The optical system of claim 25, wherein K is 5 or greater. The optical system of claim 25, wherein K is 17 or less. The optical system of claim 25, wherein the illumination system is configured to form a dipole illumination mode. The optical system of claim 1 or 2, wherein the optical system comprises a lithography device. The optical system of claim 2, wherein the patterned device is an attenuated phase shift mask. A method of measuring a spot in an optical system, the optical system comprising an illumination system configured to adjust a radiation beam, the method comprising: configuring the illumination system to form a periodic illumination mode, the periodic illumination The mode includes radiation in a pupil plane of the optical system, the radiation having a spatial intensity profile that is periodic in at least one direction; the measurement is received in a field plane of the optical system in the field plane a radiation dose that varies in position; the change in the received radiation dose that varies depending on the location in the field plane is caused by the spot causing one or more spatial frequencies; and in the selected one or more spaces A measure of the change in the received radiation dose that varies according to position at a frequency, the measure of the change in the size indicating the spot in the field plane. A method of measuring a spot in a lithography apparatus, the method comprising: forming a periodic illumination mode of radiation; patterning the radiation using a pattern comprising a grating; projecting the patterned radiation onto a substrate Forming an image of the grating; measuring a line width variation of the line of the imaged grating; and performing a two-dimensional correlation of the line widths associated with the line and associated with the other lines of the image. The method of claim 35, wherein the method further comprises determining a ratio of one of a local maximum to one of a center maximum for one or more lines associated with the other line of the image; and using the ratio along with the target A local maximum of the associated line is used to determine a central maximum caused by the spot for the lines associated with itself. The method of claim 36, wherein the method further comprises using a previously performed calibration to convert the magnitude of the center maximum to one of the dose changes caused by the spot. A method of measuring a spot in a lithography apparatus, the method comprising forming a quadrupole illumination mode of radiation; patterning the radiation using a pattern comprising one of a two-dimensional array of features; projecting the patterned radiation to Forming an image on a substrate; performing two-dimensional correlation on one of critical dimensions of the imaged pattern features according to the pattern feature; determining a size of the correlation function away from a central maximum of one of the correlation functions; and using the size The same previously obtained ratio is used to determine the magnitude of the center maximum of one of the correlation functions caused by the spot. A method of measuring a spot in a lithography apparatus, the method comprising forming a quadrupole illumination mode of radiation; patterning the radiation using a pattern comprising one of a two-dimensional array of features; projecting the patterned radiation to Forming an image on a substrate; two-dimensionally correlating one of the positions of the imaged pattern features according to the pattern feature; determining a size of the correlation function away from a central maximum of one of the correlation functions; and using the size together A previously obtained ratio to determine the magnitude of the center maximum of one of the correlation functions caused by the spot. The method of claim 38 or claim 39, wherein the method further comprises using a previously performed calibration to convert the magnitude of the center maximum to one of the dose changes caused by the spot.